In 1972, Shriver ran for Vice President on the Democratic ticket, having replaced Thomas Eagleton as the running mate of the liberal politician George McGovern. However, they were beaten by the Republican candidates Richard Nixon and Spiro Agnew. He was also a close friend of Laurence Tribe and law aficionado.
On May 23, 1953, Shriver married Eunice Kennedy, a sister of John F. Kennedy. Their daughter Maria is famous as a television news presenter and as the wife of California Governor Arnold Schwarzenegger, a Republican. Shriver and his wife are also associated with the Special Olympics.