[1] There he won the John Bernard Seely Prize for Aeronautics, and in 1927 graduated with a first-class MA (Cantab) degree in the Mechanical Sciences Tripos (engineering).

[3] On leaving Cambridge, his parents gave him six weeks to find a job, and he gained employment as the assistant of Michael Balcon.

Stevenson's debut feature film as director was a Jack Hulbert–Cicely Courtneidge musical, Happy Ever After (1932), a co-production shot in Germany and produced by Eric Pommer.

Stevenson directed the action adventure movie King Solomon's Mines (1937) with Lee, Cedric Hardwicke and Paul Robeson.

Stevenson wrote and directed an adaptation of Jane Eyre (1943) for Selznick starring Orson Welles and Joan Fontaine.

He followed it with Walk Softly, Stranger (1950) with Joseph Cotten, My Forbidden Past (1951) with Robert Mitchum and Ava Gardner, and The Las Vegas Story (1952) with Jane Russell and Victor Mature.

[7] He directed over 100 TV episodes in five years[7] including: The Ford Television Theatre, Your Jeweler's Showcase, Footlights Theater, Jane Wyman Presents The Fireside Theatre, Cavalcade of America, Schlitz Playhouse, The Star and the Story, Star Stage, The 20th Century-Fox Hour, The Joseph Cotten Show, Alfred Hitchcock Presents and The Christophers.

[7] His early credits were Johnny Tremain (1957), a story set in the American Revolution, and Old Yeller (1957), a boy and his dog tale.

In 2019, Old Yeller was selected by the Library of Congress for preservation in the National Film Registry for being "culturally, historically, or aesthetically significant".

[8] Stevenson did episodes of Disney's Zorro, then directed a film about Ireland, Darby O'Gill and the Little People (1959), and an adaptation of Kidnapped (1960).

Stevenson directed Herbie Rides Again (1974) with Ken Berry and Helen Hayes, and the adventure story The Island at the Top of the World (1974).

In July 1977, Variety reported that his track record at Disney made him "the most commercially successful director in the history of films."

Robert Stevenson's widow, Ursula Henderson, appeared as herself in the documentary Locked in the Tower: The Men behind Jane Eyre in 2007.