Music

1934 
Who won: One Night of Love, Columbia Studio Music Department, Louis Silvers, head of department (Scoring); "The Carioca," from The Gay Divorcee, Music by Con Conrad; Lyrics by Herb Magidson (Song)
Who should have won: The Gay Divorcee, RKO Radio Studio Music Department, Max Steiner, head of department (Scoring); "Let's Fall in Love," from Let's Fall in Love, Music by Harold Arlen; Lyrics by Ted Koehler

1935
Who won: The Informer, RKO Radio Studio Music Department, Max Steiner, head of department (Score by Max Steiner) (Scoring); "Lullaby of Broadway" from Gold Diggers of 1935, Music by Harry Warren; Lyrics by Al Dubin (Song)
Who should have won: Captain Blood, Warner Bros.-First National Studio Music Department, Leo Forbstein, head of department (Score by Erich Wolfgang Korngold) (Scoring); "Cheek to Cheek" from Top Hat, Music and Lyrics by Irving Berlin (Song) 

1936 
Who won: Anthony Adverse,  Warner Bros. Studio Music Department, Leo Forbstein, head of department (Score by Erich Wolfgang Korngold) (Scoring); "The Way You Look Tonight" from Swing Time, Music by Jerome Kern; Lyrics by Dorothy Fields (Song) 

1937 
Who won: One Hundred Men and a Girl, Universal Studio Music Department, Charles Previn, head of department (no composer credit) (Scoring); "Sweet Leilani" from Waikiki Wedding. Music and Lyrics by Harry Owens (Song)
Who should have won: Shall We Dance, RKO Radio Studio Music Department, Nathaniel Shilkret, musical director (score by George Gershwin) (Scoring); "They Can't Take That Away From Me" from Shall We Dance. Music by George Gershwin; Lyrics by Ira Gershwin (Song)

1938 
Who won: Erich Wolfgang Korngold, The Adventures of Robin Hood (Original Score); Alfred Newman, Alexander's Ragtime Band (Scoring); "Thanks for the Memory," from The Big Broadcast of 1938; music by Ralph Rainger, lyrics by Leo Robin (Song) 
Who should have won: "Our Love Is Here to Stay," from The Goldwyn Follies; music by George Gershwin, lyrics by Ira Gershwin (Song)

1939 
Who won: Herbert Stothart, The Wizard of Oz (Original Score); Richard Hageman, Frank Harling, John Leipold, Leo Shuken, Stagecoach (Scoring); "Over the Rainbow," from The Wizard of Oz; music by Harold Arlen, lyrics by E.Y. Harburg (Song) 
Who should have won: Sergei Prokofiev, Alexander Nevsky (Original Score); Herbert Stothart, The Wizard of Oz (Scoring)

1940 
Who won: Leigh Harline, Paul J. Smith, Ned Washington, Pinocchio (Original Score); Alfred Newman, Tin Pan Alley (Scoring); "When You Wish Upon a Star," from Pinocchio; music by Leigh Harline, lyrics by Ned Washington (Song) 
Who should have won: Aaron Copland, Our Town (Original Score); Leigh Harline, Paul J. Smith, Ned Washington, Pinocchio (Scoring)

1941 
Who won: Bernard Herrmann, All That Money Can Buy (Music Score for a Dramatic Picture); Frank Churchill, Oliver Wallace, Dumbo (Scoring of a Musical Picture); "The Last Time I Saw Paris," from Lady Be Good; music by Jerome Kern, lyrics by Oscar Hammerstein II (Song)

1942 
Who won: Max Steiner, Now, Voyager (Music Score for a Dramatic or Comedy Picture); Ray Heindorf, Heinz Roemheld, Yankee Doodle Dandy (Scoring of a Musical Picture); "White Christmas," from Holiday Inn; music and lyrics by Irving Berlin (Song)

1943 
Who won: Alfred Newman, The Song of Bernadette (Music Score of a Dramatic or Comedy Picture); Ray Heindorf, This Is the Army (Scoring of a Musical Picture); "You'll Never Know," from Hello, Frisco, Hello, music by Harry Warren, lyrics by Mack Gordon
Who should have won: George Bassman, Roger Edens, Hall Johnson, Georgie Stoll, Cabin in the Sky (Scoring of a Musical Picture); "That Old Black Magic," from Star Spangled Rhythm, music by Harold Arlen, lyrics by Johnny Mercer

1944 
Who won: Max Steiner, Since You Went Away (Music Score of a Dramatic or Comedy Picture); Morris Stoloff, Carmen Dragon, Cover Girl (Scoring of a Musical Picture); "Swinging on a Star," from Going My Way, music by James Van Heusen, lyrics by Johnny Burke
Who should have won: David Raksin, Laura (Music Score of a Dramatic or Comedy Picture); Georgie Stoll, Meet Me in St. Louis (Scoring of a Musical Picture); "Spring Will Be a Little Late this Year," from Christmas Holiday, music and lyrics by Frank Loesser

1945 
Who won: Miklos Rozsa, Spellbound (Music Score of a Dramatic or Comedy Picture); Georgie Stoll, Anchors Aweigh (Scoring of a Musical Picture); "It Might As Well Be Spring," from State Fair, music by Richard Rodgers, lyrics by Oscar Hammerstein II (Song)
Who should have won: "Accentuate the Positive," from Here Come the Waves, music by Harold Arlen, lyrics by Johnny Mercer 

1946 
Who won: Hugo Friedhofer, The Best Years of Our Lives (Music Score of a Dramatic or Comedy Picture); Morris Stoloff, The Jolson Story (Scoring of a Musical Picture); "On the Atchison, Topeka, and the Santa Fe," from The Harvey Girls, music by Harry Warren, lyrics by Johnny Mercer
When it should have gone to: William Walton, Henry V (Music Score of a Dramatic or Comedy Picture) 

1947 
Who won: Miklos Rozsa, A Double Life (Music Score of a Dramatic or Comedy Picture); Alfred Newman, Mother Wore Tights (Scoring of a Musical Picture); "Zip-A-Dee-Doo-Dah," from Song of the South, music by Allie Wrubel, lyrics by Ray Gilbert (Song). 
When it should have gone to: Bernard Herrman, The Ghost and Mrs. Muir (Music Score of a Dramatic or Comedy Picture); "Time After Time," from It Happened in Brooklyn, music by Jule Styne, lyrics by Sammy Cahn (Song)

1948 
Who won: Brian Easdale, The Red Shoes (Music Score of a Dramatic or Comedy Picture); Johnny Green, Roger Edens, Easter Parade (Scoring of a Musical Picture); Jay Livingston, Ray Evans, music and lyrics, "Buttons and Bows" from The Paleface (Song)