Born at Maidstone, Kent, he was the son of another Sir Richard Wydeville or Wydevill, chamberlain to the Duke of Bedford. After the duke died, the younger Richard married the widowed duchess, Jacquetta of Luxembourg (1416-1472). This was initially a secret marriage for which the couple were fined when it came to public notice.
Originally a mere squire from Grafton, Richard was considered "the handsomest man in England" and rose to become the squire of Henry V at the Battle of Agincourt in which the house of Lancaster conquered France. He managed to keep the king's lucky totem of a squirrel's tail tied to a lance "always within sight of the king" during the battle, and was knighted afterwards.
He was created Baron Rivers by Henry VI on May 9, 1448. Initially, he was on the Lancastrian side in the Wars of the Roses, but he later changed allegiances, and became a Yorkist, once he was convinced that the Lancastrian cause was lost, and he reconciled himself to the new king, his future son-in-law. After the marriage of his daughter, Elizabeth Woodville, widow of Sir John Grey of Groby, to Edward IV on May 1, 1464, he was created Earl Rivers (1466), and appointed Lord Treasurer by his new son-in-law.
The power of this new family was very distasteful to the old baronial party, and especially so to the Earl of Warwick. Early in 1468, the Riverses' estates were plundered by Warwick's partisans, and the open war of the following year was aimed to destroy the Woodvilles. After the king's defeat at the Battle of Edgecote Moor on 26 July, 1469, Rivers and his second son, John, were taken prisoners at Chepstow. Following a hasty show trial, they were beheaded at Kenilworth. His eldest son, Anthony succeeded him in the earldom.
Lord Rivers had a large family. His third son, Lionel, (d. 1484), became the Bishop of Salisbury. All his daughters made great marriages: Catherine Woodville, the fifth child, was wife of Henry Stafford, 2nd Duke of Buckingham.