The work is a fictional historical essay dealing with the preamble to the events described in Tolkien's epic novel The Lord of the Rings, and the events themselves, in the style of The Silmarillion. As the name implies, the events of the essay are focused around magical artifacts: the Rings of Power, and also the history of the Second and Third Ages of Middle Earth. The fact that those events are explored in a mere handful of pages suggests that if the events described in the rest of The Silmarillion had been written in the style of The Lord of the Rings they would have filled hundreds of volumes.
After Tolkien's death in 1973, Christopher Tolkien completed this part, assisted by Guy Gavriel Kay. Of the Rings of Power and the Third Age bears some similarities to Elrond's narrative in The Fellowship of the Ring during the chapter "The Council of Elrond"; both do not divulge any details about how Arnor was destroyed and how Gondor became kingless. The closeness is perhaps intentional; as Elrond told the Second and Third Age through his eyes, The Silmarillion is supposed to be told through the point of the view of the Eldar.
Information on the background and development of this essay can be found in The Treason of Isengard.
However, not all of Middle Earth remained under Sauron's sway. Those Elves who had survived the vicissitudes of the First Age founded a new kingdom in Eregion, and during the Second Age, the Elves of Eregion forged many magical rings, including nineteen Rings of Power with the aid of Sauron. At this time Sauron was still able to put on a fair appearance and managed to fool the elves into believing his intentions were good. But Sauron had deceived them, for in secret he made the One Ring for himself, which was the master of the rest, in order to enslave them, and all the other peoples of Middle Earth.
However Sauron's plan failed: the Elves discovered his plot and discarded their Rings until they could be shielded from his influence. Sauron then waged war upon the Elves, capturing all the Rings of Power except three. While many Elves were killed and the kingdom in Eregion destroyed, the Men of Númenor helped the Elves and repelled Sauron. After the war, Sauron distributed seven rings to Dwarves and Nine to Men. The dwarves proved immune to his influence, becoming only inflamed with greed for gold, but Men proved weaker. The nine kings who had received the rings fell under Sauron's sway, becoming in the end the wraith-like Nazgûl.
Only a few survivors leave Númenor before it is too late, and led by Elendil the Tall and his two sons Isildur and Anárion, they settle in Middle-earth. They create realms governed in Númenórean style — Elendil rules over Arnor in the North, and Isildur and Anárion rule together in the great country of Gondor in the South. However, Sauron survived the disaster too, and although he has lost his fair appearance, both he and his One Ring return safely to his stronghold of old in the land of Mordor.
Years pass, and Sauron, who had renewed his might, decides to attack the new realms while they were still weak. His onslaught fails, however, and Elendil, his sons, and the Elven kings fight back. For many years the great coalition (The Last Alliance of Elves and Men, as it became known) besiege Mordor. At last the host breaks through into Sauron's fortress of Barad-dûr. Anárion died first before Sauron broke the siege and the mighty king of the Elves, Gil-galad challenges Sauron to a duel, but too is killed. Finally Elendil fights Sauron, and though he is mortally wounded he manages to overcome Sauron before he dies. Isildur, Elendil's son, approaches Sauron's body and cuts off his finger with the One Ring, breaking Sauron's power and causing his spirit to depart from his body, and Sauron never after takes physical form.
Heirs of royal blood are chosen to lead Arnor and Gondor. For a millennium, both realms enjoy relative freedom and prosperity. However afterwards, Arnor became subject to attacks from the north-eastern kingdom of Angmar, a kingdom that was ruled by the Witch-king, leader of the Ringwraiths. More and more people flee from the North, and although Angmar is defeated by the beginning of the third millennium of Third Age, Arnor is no more. Its people are scattered, and its royalty decrease in number and fame; however they remain true to their Númenórean descent. They become the Rangers of the North, protecting the paths of the North from the menace from the East.
Meanwhile, Gondor prospers for much of the Third Age. However in the beginning of its third millennium, this begins to change. Gondor is assailed by Orcs and Men from the nearby Mordor. For a long time, no one suspects that the same force that had driven the attacks upon Arnor is now fighting Gondor.
After this, it is made clear that Gandalf bore the Red Ring, Narya and that Galadriel and Elrond had the other two rings. Aragorn son of Arathorn (direct descendant of many of the characters appearing earlier in the printed Silmarillion) is briefly mentioned as returning to claim the kingship and fighting a great field of battle before the City of Gondor, though he is only referred to as the "Heir of Isildur".
The essay finishes with the departure of the Keepers of the Rings from the Grey Havens (at the end of Lord of the Rings) and then the sailing of the Last Ship of the Eldar ever to leave Middle-earth. Thus, "an end had come to the Eldar, of story and of song".