The 21st Grammy Awards were held in 1979, and were broadcast live on American television. They recognized accomplishments by musicians from the year 1978.

Award winners:

• Record of the Year
  • Phil Ramone (producer) & Billy Joel for "Just the Way You Are"

• Album of the Year
  • Broadway Eddie , Richard Finch , Albhy Galuten , K.G. Productions , Ron Kersey , Arif Mardin, Bobby Martin , Bill Oakes , Freddie Perren, Karl Richardson , William Salter , Thomas J. Valentino (producers), Bee Gees, Ralph MacDonald , David Shire (producers and artists), Don Renaldo (conductor), Yvonne Elliman, K.C. and the Sunshine Band, Kool & the Gang, Walter Murphy , Tavares & Trammps for Saturday Night Fever

• Song of the Year
  • Billy Joel for "Just the Way You Are"

• Best New Artist
  • A Taste of Honey

Children's

• Best Recording for Children
  • Jim Henson (producer) for The Muppet Show performed by The Muppets

Classical

• Best Classical Orchestral Performance
  • Michel Glotz (producer), Herbert von Karajan (conductor) & the Berlin Philharmonic Orchestra for Beethoven: Symphonies (9) (Complete)
• Best Classical Vocal Soloist Performance
  • Luciano Pavarotti for Luciano Pavarotti - Hits From Lincoln Center
• Best Opera Recording
  • George Sponhaltz , John Coveney (producers), Julius Rudel (conductor), Beverly Sills, Alan Titus & the New York City Opera Orchestra for Lehár: The Merry Widow
• Best Choral Performance, Classical (other than opera)
  • Georg Solti (conductor), Margaret Hillis (choir director) & the Chicago Symphony Orchestra & Chorus for Beethoven: Missa Solemnis
• Best Classical Performance Instrumental Soloist or Soloists (with orchestra)
  • Eugene Ormandy (conductor), Vladimir Horowitz & the New York Philharmonic for Rachmaninoff: Con. No. 3 in D Minor for Piano (Horowitz Golden Jubilee)
• Best Classical Performance, Instrumental Soloist(s) (without orchestra)
  • Vladimir Horowitz for The Horowitz Concerts 1977/78
• Best Chamber Music Performance
  • Itzhak Perlman & Vladimir Ashkenazy for Beethoven: Sonatas for Violin and Piano
• Best Classical Album
  • Christopher Bishop (producer), Carlo Maria Giulini (conductor), Itzhak Perlman & the Chicago Symphony Orchestra for Brahms: Concerto For Violin in D

Comedy

• Best Comedy Recording
  • Steve Martin for A Wild and Crazy Guy

Composing and arranging

• Best Instrumental Composition
  • John Williams (composer) for "Theme From Close Encounters of the Third Kind"
• Best Album of Original Score Written for a Motion Picture or a Television Special
  • John Williams (composer) for Close Encounters of the Third Kind
• Best Instrumental Arrangement
  • Quincy Jones & Robert Freedman (arrangers) for "The Wiz Main Title - Overture Part One" performed by various artists
• Best Arrangement Accompanying Vocal(s)
  • Maurice White (arranger) for "Got to Get You Into My Life" performed by Earth, Wind & Fire
• Best Arrangement For Voices
  • The Bee Gees (arrangers) for "Stayin' Alive"

Country

• Best Country Vocal Performance, Female
  • Dolly Parton for Here You Come Again
• Best Country Vocal Performance, Male
  • Willie Nelson for "Georgia on My Mind"
• Best Country Performance by a Duo or Group with Vocal
  • Waylon Jennings & Willie Nelson for "Mamas Don't Let Your Babies Grow Up to Be Cowboys"
• Best Country Instrumental Performance
  • Asleep at the Wheel for "One O'Clock Jump"
• Best Country Song
  • Don Schlitz (songwriter) for "The Gambler" performed by Kenny Rogers

Folk

• Best Ethnic or Traditional Recording
  • Muddy Waters for I'm Ready

Gospel

• Best Gospel Performance, Traditional
  • The Happy Goodman Family for Refreshing
• Best Gospel Performance, Contemporary or Inspirational
  • Larry Hart for "What a Friend"
• Best Soul Gospel Performance, Traditional
  • Mighty Clouds of Joy for Live and Direct
• Best Soul Performance, Contemporary
  • Andrae Crouch for Live in London performed by Andrae Crouch &the Disciples
• Best Inspirational Performance
  • B.J. Thomas for Happy Man

Historical

• Best Historical Repackage Album
  • Michael Brooks (producer) for The Lester Young Story, Vol. 3

Jazz

• Best Jazz Instrumental Performance, Soloist
  • Oscar Peterson for Montreaux '77 - Oscar Peterson Jam
• Best Jazz Instrumental Performance, Group
  • Chick Corea for Friends
• Best Jazz Instrumental Performance, Big Band
  • Mel Lewis & Thad Jones for Live in Munich
• Best Jazz Vocal Performance
  • Al Jarreau for All Fly Home

Latin

• Best Latin Recording
  • Tito Puente for Homenaje a Beny More

Musical Show

• Best Cast Show Album
  • Thomas Z. Shepard (producer) & various artists for Ain't Misbehavin'

Packaging and Notes

• Best Album Package
  • Johnny B. Lee & Tony Lane (art directors) for Boys in the Trees performed by Carly Simon
• Best Album Notes
  • Michael Brooks (notes writer) for A Bing Crosby Collection, Vols. I & II performed by Bing Crosby

Pop

• Best Pop Vocal Performance, Female
  • Anne Murray for "You Needed Me"
• Best Pop Vocal Performance, Male
  • Barry Manilow for "Copacabana (At the Copa)"
• Best Pop Vocal Performance by a Duo or Group
  • The Bee Gees for Saturday Night Fever
• Best Pop Instrumental Performance
  • Chuck Mangione for Children of Sanchez

Production and engineering

• Best Engineered Recording, Non-Classical
  • Al Schmitt & Roger Nichols (engineers) for "FM (No Static At All)" performed by Steely Dan
• Best Engineered Recording, Classical
  • Arthur Kendy , Edward T. Graham , Ray Moore (engineers), Pierre Boulez (conductor) & the New York Philharmonic for Varese: Ameriques/Arcana/Ionisation (Boulez Conducts Varese)
• Producer of the Year
  • The Bee Gees, Albhy Galuten & Karl Richardson

R&B

• Best R&B Vocal Performance, Female
  • Donna Summer for "Last Dance"
• Best R&B Vocal Performance, Male
  • George Benson for "On Broadway"
• Best R&B Vocal Performance by a Duo, Group or Chorus
  • Earth, Wind & Fire for All 'n All
• Best R&B Instrumental Performance
  • Earth, Wind & Fire for "Runnin' "
• Best Rhythm & Blues Song
  • Paul Jabara (songwriter) for "Last Dance" performed by Donna Summer

Spoken

• Best Spoken Word Recording
  • Orson Welles for Citizen Kane