Richard Jr. appeared in a few plays at Brooks Preparatory School, but initially had no intention of becoming an actor and wanted to be an architect.

After graduating from Brooks School and Princeton University, where he studied architecture, he moved to Hollywood and landed a role opposite Sam Elliott in the 1976 film Lifeguard.

[2] Stevenson became well known from starring with teen heartthrob Shaun Cassidy in The Hardy Boys/Nancy Drew Mysteries series, produced by Glen A. Larson's production company through MCA-Universal Television (now NBCUniversal) under license from the Stratemeyer Publication Syndicate, from 1977 to 1979 on ABC.

[2] In 1983, he co-starred in the movie Stroker Ace as Burt Reynolds's brash race-car driving nemesis, Aubrey James.

[8][9] Stevenson married celebrity chef Lisa Schoen on September 29, 2018, at Demetria Vineyards in Los Olivos, California.