During his youth, Tywin managed to single-handedly restore his family's honor and fortunes from near ruin, and from then on dedicated all his efforts to maintaining Lannister prestige. A minstrel song, The Rains of Castamere, was written to celebrate his triumph over two rebellious bannermen, the Reynes and the Tarbecks, whose lines he extingiushed root and stem for their dissent. He also unilaterally annulled his son's marriage when Tyrion wed Tysha, a crofter's daughter, for love (see Tyrion's heading below for more details), an act which would have later repercussions toward his death.
Though ruthless, Tywin Lannister was also an able and shrewd ruler who brought great prosperity during his dual tenures as Hand of the King. He was especially talented at the raising of funds, leading to persistent rumors of a "Midas touch" and even the whispered jest that he must "shit gold". His daughter Cersei once reminisced that the common folk cheered twice as loud for him as they did for their actual king, Mad Aerys II (though only half as loud as they did for Rhaegar). He was highly insensitive to those around him, however, expecting duty and obedience from all and having no patience with anything less; in Tyrion's narrative, he mentions (more than once) that Tywin never, ever smiles. Though his children respected him, none of them were ever able to live up to his expectations for them, which caused friction between him and his children while he was alive.
He was a powerful Hand of the King for a long time under Aerys II until Aerys' increasing paranoia and jealousy drove the two into several bitter disagreements. After Aerys refused to marry Cersei to his heir, Prince Rhaegar, and raised Jaime to the Kingsguard without Tywin's permission, Tywin resigned the position of Hand and returned to his own lands, the most recent Hand to leave the office with lands, titles and person intact. During Robert's Rebellion Tywin remained at Casterly Rock, taking no side until after Robert's victory at the Battle of the Trident. After the battle, Tywin mustered his forces and rode for the capital of King's Landing. While Aerys was convinced that Tywin had come to aid him and opened the gates of the city, Tywin's forces turned their cloaks and sacked the city, and knights sworn to him slew Rhaegar's wife and children. As Tywin explained to Tyrion years later, "No one could doubt that we had forsaken House Targaryen forever."
After Robert Baratheon's death, Tywin was made Hand of the King for Joffrey, his grandson. For much of the next year he conducted war against House Stark and had his son Tyrion serve as Hand in his stead. When his surprise withdrawal to attack Stannis led to the victory of House Lannister at the Battle of the Blackwater and an alliance with House Tyrell, he resumed his position as Hand until Joffrey's death by poison at Joffrey's wedding. When his son Tyrion was accused of the crime Tywin presided over the case, and he eventually sentenced Tyrion to death after Tyrion's champion was slain in a trial by combat. However, Tyrion was freed by Jaime, and not long later slew Tywin in his bedchamber.
Cersei has shared an incestuous relationship with her brother Jaime since they were youths, and continued it throughout her fifteen-year marriage to King Robert, made possible both by Cersei's craftiness and Robert's philandering nature. Her three children were all a product of this incest, rather than her husband King Robert; this secret, when discovered by Jon Arryn, Eddard Stark and Stannis Baratheon, was used as a political tool during the War of the Five Kings.
Throughout the series, Cersei has increasingly climbed the ladder of power. After arranging the death of her husband, Cersei put her 13-year-old son Joffrey on the throne, despite accusations of bastardy, and ruled as his Queen Regent. However, Tywin promptly put Tyrion in the position of Hand of the King, and from there Tyrion was able to curtail much of her policy, a practice which Tywin continued upon his assumption of the office. They did so because Cersei is not, in fact, a very good ruler. Her brother Jaime describes her thusly:
[Cersei] liked to think of herself as Lord Tywin with teats, but she was wrong. Their father had been as relentless and implacable as a glacier, where Cersei was all wildfire, especially when thwarted. ... She does not lack for wits, but she has no judgment, and no patience. A Feast for Crows, pg. 234 (hardcover)
When Joffrey and Tywin were murdered in quick succession, the checks on her claim to power were cleared. She resumed her position as Regent over her son, the eight-year-old King Tommen, who was entirely obedient to her will, and became queen in all but name. As the eldest child of Tywin, she was also acknowledged as the Lady of Casterly Rock by her uncle Kevan. Thus empowered and unrestricted, Cersei felt she had the opportunity to prove herself an even better ruler than her father. She began her new regime by filling all of the positions on Tommen's Small Council with her own supporters and agents, disregarding the previous arrangements made by Tywin and well-meaning (if blunt) advice from Kevan. The changes she made to the small council along with some of the men she choose to fill its positions were not held in high regard by many of the lords and smallfolk which led to many referring to the small council as "the smallest council".
Cersei grew to suspect that her powerful Tyrell allies, now relatives through Tommen's marriage, were trying to seize control of the kingdom. She commenced a campaign of intrigue to remove all the Tyrells in King's Landing from positions of influence and authority, including her son's wife Margaery, and Loras, a member of the Kingsguard. She thus alienated Jaime, who abandoned her to her political paranoia. She refused to honor the debts owed by the Crown, angering powerful institutions such as the Iron Bank of Braavos and the Faith. With the monies owed, she constructed a new royal fleet of warships and gave command to Aurane Waters, a sellsail of considerable charm but questionable expertise and loyalty. In an attempt to alleviate the crown's debts and gain more protection from her purported enemies, she allowed the High Septon to revive the Faith Militant, ignoring its history of causing trouble for monarchs. She also took the disgraced former Maester Qyburn into her service, using him as a torturer and allowing him to conduct immoral experiments on human subjects.
She tried to ensnare Margaery Tyrell by telling Osney Kettleblack to seduce her, but the attempt failed as Margaery did not respond to his seduction with anything other than teasing. Thereafter she tortured Margaery's singer (the Blue Bard) into admitting to having sex with Margaery Tyrell and her companions; she also had Osney (who was only truly interested in sex with Cersei) go to the Great Sept and confess to having bedded Margaery Tyrell. This led to Margaery's arrest by the High Septon of the Faith. However, Cersei's plan backfired when Osney, arrested by the High Septon and tortured, revealed the truth about Cersei's plan, as well as the fact that the previous High Septon had been murdered on her command. Cersei was arrested and detained to await trial. Her own ministers abandoned her and seized control of the government while she was kept prisoner in the Great Sept of Baelor. They recalled her uncle Kevan to fill her position as regent, while her new lord admiral absconded with the costly new fleet. Accused of capital crimes, her only hope lay in a Kingsguard champion to stand for her in a trial by combat. She sent an emotional summons to Jaime, which he burned and to which he has not replied.
Cersei has been haunted since childhood by a prophecy given to her by a maegi. This prophesy correctly predicted the death of a childhood friend, her unrequited love for Rhaegar Targaryen, and her marriage (and mutual infidelity) with Robert. It also predicts that all three of her children will be crowned, but that all three will die before her. Everything that she has will be taken away by a younger and more beautiful queen, and then her valonqar (Valyrian for "little brother" or "younger brother") will strangle her to death. Cersei believes (whether correctly or not) that the younger, more beautiful queen is Margaery Tyrell and the valonqar is Tyrion Lannister.
Daven swore a holy oath not to cut his hair until he avenged his father's death on Rickard Karstark. After Robb executed Rickard for treason, Daven still refused to cut his hair. He was given orders to lay siege to Riverrun and appointed Warden of the West. Daven, despite being a very competent commander, struggled against the questionable loyalty of the lords of the Trident under his command and proved unable to make progress in the siege due to the bitterness between the Frey, river lord & Lannister commanders.
The war has not treated Genna gently; of her four sons, two have been killed: Cleos Frey, her firstborn, who was killed as he was escorting Jaime and Brienne from Riverrun and Tion Frey, her third son, who was killed by the Karstarks at Riverrun while a captive.
Upon the death of Robb Stark, House Tully was dispossessed of Riverrun, which was awarded to Genna, her Frey husband and her surviving children. They acquired the castle after the submission of Edmure Tully, who was taken prisoner at the Red Wedding.
Jaime was an immensely talented warrior from his youth, fighting gallantly against the Kingswood Brotherhood (an outlaw band) and was invited to join the Kingsguard at the age of 15, becoming its youngest inductee. He agreed to the appointment because of the honor involved, and also to be close to Cersei again (he loving her incestuously), as Tywin had taken her to court with him to match her with a suitable suitor (preferably Rhaegar Targaryen). However, within a day of his appointment, Jaime discovered that Aerys, paranoid of Tywin's power, had extended the invitation to turn him into a hostage and deprive Tywin of his heir. Furthermore, Tywin, slighted by this and by Aerys' refusal to wed Rhaegar to Cersei (the crown prince eventually wed Elia of Dorne), resigned his office of Hand and returned with Cersei to Casterly Rock, separating the erstwhile lovers once again. Finally, it became endlessly clear to Jaime that Aerys deserved his moniker ("the Mad"), especially after witnessing the deaths of Brandon and Rickard Stark.
Shortly before the Sack of King's Landing, Jaime learned that Aerys planned to immolate the city with wildfire should it be taken by enemy forces, killing not only the rebellious army but all its citizens as well. To prevent this mass slaughter, he slew Aerys, as well as the infrastructure the king had placed to ensure his orders was carried out; Jaime later reflected that he is often reviled for what he (Jaime) considers his finest act. Faced with scorn for his oathbreaking ways, Jaime embraced the arrogant and amoral personality people seemed to expect from him.
After Cersei became queen, Jaime fathered all of her children. He attempted to protect their secret at Winterfell by throwing the seven-year old Bran Stark from a window; this, among other factors, incited the War of the Five Kings that followed. He gave battle to Robb Stark at the Whispering Wood and was captured there, subsequently spending much of the war imprisoned at the Tully stronghold of Riverrun. He was eventually freed by Catelyn Stark under oath to (among other things) exchange his life for those of her daughters (Sansa and Arya), and never take arms against the Starks or Tullys again. Catelyn appointed Brienne of Tarth to escort him to King's Landing. At once annoyed and impressed by Brienne's honor and idealism, Jaime still attempted to kill her out of simple malice and arrogance. Brienne was able to defend herself, but would later admit that if Jaime's hands had not been shackled she would not have had any hope of victory.
During Jaime and Brienne's capture by the Brave Companions, Jaime's sword hand was cut off. Deprived of his identity-defining martial prowess, troubled by Brienne's noble behavior, and realizing he no longer liked having (in his own words) "shit for honor," Jaime began to re-evaluate his life, beginning with risking his own life to rescue Brienne from the Brave Companions. When he returned safely to King's Landing, he assumed the office of Lord Commander of the Kingsguard and took his post seriously. His newfound responsibilities caused problems with his family relationships: conflicted by the discovery of Cersei's infidelity, Jaime's feelings toward Cersei soured; he also refused to leave the Kingsguard and become Tywin's heir, causing his father to disown him. Going completely against his family, he charged Brienne to find the missing Sansa Stark and keep her safe from the wrath of House Lannister. He gave her a Valyrian steel longsword his father had fashioned for him out of Ned Stark's greatsword "Ice," and bade her name it "Oathkeeper." Finally, he rescued his brother Tyrion from execution and admitted to betraying him during a traumatic moment in Tyrion's youth.
Jaime's oath to Catelyn was put in jeopardy when he went to Riverrun to end Brynden Tully's resistance. He managed to take the castle bloodlessly by releasing the prisoner Lord Edmure Tully and threatening the life of his unborn child should he refuse to yield the castle. Though he succeeded in keeping his oath to Catelyn, the incident added to Jaime's already-monstrous reputation as kingslayer, child-killer, and sister-lover.
The end of A Feast for Crows shows him commanding that Cersei's letter asking him to save her life be thrown into the fireplace. Whether he is actually ignoring her pleas or simply destroying the letter, which might otherwise be used as evidence to prove their incestuous relationship, remains to be seen.
After Tywin's death, Cersei offered him the position of Hand of the King. However he did not trust in Cersei's leadership and said he would only take the position if she returned to Casterly Rock and gave him the regency. After her refusal he refused the position of Hand and accused Cersei of being both a poor leader and mother. He quickly became alienated to his immediate family. He believed Tyrion to be a murderer and came to believe the rumors of incest about Cersei and Jaime. His eldest son, Lancel, became a religious fanatic and abandoned the estate Kevan had won for him. Kevan was also angered that Daven received the title of Warden of the West over him, and refused to add his forces to his cousin's at Riverrun, and returned to the West to see his younger son Martyn. After Cersei's imprisonment, the Small Council named him Regent of the King. It is thus far unknown whether he will accept it.
In his few appearances since Lord Tywin's death, Kevan has shown himself to be a competent administrator in his own right. Tywin may have been more strong-willed, but Kevan has proven to be just as clear-sighted (doubtless because of the decades he spent as Tywin's right hand man). While not a lord in his own right, his strategic thinking and significant retinue and personal wealth make him a man of significant standing.
Lancel idolized his cousin Jaime to the point that he eagerly participated in Cersei's plans to kill Robert so that he too could become a Kingslayer. He served Robert an unusually potent wine, known as "strongwine" during a hunting expedition, causing the King to be gored by a boar. After Robert's death, Lancel was knighted. Cersei later took him as a lover while Jaime went to war due to his resemblance to her brother. At the Battle of the Blackwater he guarded Joffrey until Cersei ordered Joffrey to be taken away from sight during the battle. Lancel took a serious wound in the fighting and later chastised Cersei for the damage her action caused to morale.
Lancel lingered near death for a long time and he never fully recovered from his wound. During the trauma of his recovery, Lancel experienced a spiritual reawakening. He began to feel guilt for his services to Cersei, especially of participating in the murder of King Robert. For his services at the Blackwater he was named the Lord of Darry. As part of the Frey alliance he was betrothed to a daughter of their house. Kevan took him to the Darry castle and chose his bride, Amerei Frey, whose mother was of House Darry. Lancel married Amerei but refused to consummate the marriage, spending most of his time in the sept doing penance for his sins. His behavior angered his father greatly. When word reached Lancel of the resurgence of the Warrior Sons, an order of holy knights, he renounced his castle, lands and wife and traveled to King's Landing to join them.
After the defeat of Jaime Lannister, Stafford was charged to form a new Lannister army to attack Riverrun. While training this army at Oxcross, he was taken completely unaware by King Robb Stark's army (since he had neglected to send out scouts) and killed in the ambush by Lord Rickard Karstark.
Early in life, Tyrion found himself ostracized from regular family life, and sought his own entertainment. When Tyrion was 13, he and Jaime rescued a common girl, Tysha, from a compromising situation. Tysha found Tyrion pleasing, and they married in secret, but Lord Tywin found out and explained that she was a prostitute whom Jaime had hired for Tyrion's benefit. Tywin had her repeatedly raped by his men before Tyrion's eyes, and then forced the boy to do the same. This incident scarred Tyrion, but also brought him closer to Jaime, the only person who ever showed kindness to him.
Tyrion joined the royal family on their fateful trip to Winterfell, after which he visited The Wall with Jon Snow, Eddard Stark's bastard son. On his return, he met Catelyn Stark at a roadside inn. She arrested him on suspicion of the attempted murder of Bran Stark and brought him to the Eyrie. There Lysa Arryn put him on trial for that crime, as well as the murder of Jon Arryn (he was innocent of both). He escaped punishment with the victory of his champion, the sellsword Bronn, in a trial by combat. After leaving the Eyrie, he recruited the mountain clans of the Vale into his service with hopes of using them against the Vale. Along with his new troops, he participated in the Battle of the Green Fork against Stark forces commanded by Roose Bolton.
Tywin made Tyrion his temporary replacement as Hand of the King, but forbade him from indulging in his weakness for prostitutes. Tyrion disobeyed him, secretly taking the young prostitute Shae into his service. As Hand, he entered a bitter power struggle with Cersei, but managed to consistently outplot her. He arranged the wildfire-filled ships and massive chain that decimated Stannis Baratheon's fleet during the Battle of the Blackwater and greatly contributed to the victory against Stannis. His contributions were not appreciated, however, and he took a severe facial wound in an assassination attempt during the fighting.
Upon the return of his father, Tyrion found himself demoted to Master of Coin and forced into a political marriage with Sansa Stark. Though they were married for over a month and though Tyrion grew to care for his unwilling bride, Tyrion never forced consummation on her, a decision that earned him scorn and jest in court but gratitude from his wife. The two were eventually accused of the murder of King Joffrey, but since Sansa had fled, only Tyrion stood trial; his jury was Tywin Lannister, Mace Tyrell and Prince Oberyn Martell . During the trial, Tyrion was accused and humiliated by several people, including his prostitute, Shae, who lied under incentive from Cersei. However, it was known that Gregor Clegane would be Cersei's champion in case Tyrion picked trial by combat, and the formidable duelist Oberyn Martell agreed to champion Tyrion to revenge himself against Gregor Clegane. Unfortunately, The Mountain that Rides killed the Red Viper of Dorne after a bitter fight, and Tyrion was condemned to death.
Tyrion was freed from his prison cell by his brother Jaime and a reluctant Varys. During their escape, Jaime revealed that their father had made him lie about Tysha being a prostitute, and that she was exactly what she seemed: a peasant girl who had genuinely loved Tyrion. Tyrion saw this as an unforgivable betrayal and abandoned Jaime, promising retribution if they met again. He also revealed that Cersei was "a lying whore" who was having sex with Lancel, Osmund Kettleblack "and Moon Boy for all I know" and (falsely) told Jaime that he had indeed poisoned Joffrey. Before leaving the castle, Tyrion visited his father's room via the secret tunnels and found Shae. She begged forgiveness, but Tyrion strangled her nonetheless. He then confronted his father on the privy, demanding he tell him what became of Tysha. Tywin revealed that he had not killed her, but provoked Tyrion by repeatedly calling her a whore. Tyrion slew his father with a crossbow and escaped.
Tyrion has since fled across the narrow sea, his own motives unknown even to himself. In an excerpt from A Dance with Dragons on Martin's website it is revealed that Tyrion is currently in Pentos and is staying with Illyrio Mopatis. Back in the Seven Kingdoms, Cersei has put a bounty on his head, resulting in a mass murder of dwarves and children.