Below is a list of significant 20th and 21st century composers. Each piece links directly to either a Naxos or YouTube recording of the work. While this list is by no means exhaustive, it does provide a starting point.

John Adams: (b. 1947)

• Short Ride in a Fast Machine
• Chamber Symphony
• The Death of Klinghoffer
• Shaker Loops

John Luther Adams (b. 1953)

• INUKSUIT
• Songbirdsong
• Dark Waves

Milton Babbit: (1916-2011)

• Three Compositions for Piano
• Philomel
  • First half
  • Second half

Grazyna Bacewicz: (1909-1969)

• Sonata No. 2 for solo violin
• Music for Strings, Trumpet and Percussion
• Pensieri Notturni

Samuel Barber: (1910-1981)

• String Quartet op. 11
• Knoxville Summer of 1915
• Hermit Songs

Bela Bartok: (1881-1945)

• Concerto for Orchestra
• Music for Strings, Percussion and Celeste
• Romanian Folk Dances
• String Quartet No. 3
• Viola Concerto

Alban Berg: (1885-1935)

• Wozzeck
• Violin Concerto
• Lulu

Leonard Bernstein: (1918-1990)

• West Side Story
• Candide
• On The Town

William Bolcom: (b. 1938)

• Songs of Innocence and Experience
• Graceful Ghost Rag
• I Will Breathe A Mountain
• Sonata No. 2 for Violin and piano

Pierre Boulez: (b. 1925)

• Sur Incises
• Polyphonie X
• Pli selon Pli
• Le marteau sans maitre

Benjamin Britten: (1913-1976)

• Peter Grimes
• War Requiem
• Rejoice in the Lamb

John Cage: (1912-1992)

• Sonatas and Interludes for Prepared Piano
• Music of Changes
• 4’33”

Elliott Carter: (1908-2012)

• String Quartet No. 2
• 8 Pieces for Four Timpani

Aaron Copland: (1900-1999)

• Appalachian Spring
• Rodeo
• El Salon Mexico
• Fanfare for the Common Man

John Corigliano: (b. 1938)

• Symphony No. 1
• Clarinet Concerto
• Of Rage and Remembrance

Henry Cowell: (1897-1965)

• The Banshee
• The Aeolian Harp
• 3 Irish Legends

George Crumb: (b. 1929)

• Black Angels
• Ancient Voices of Children
• Makrokosmos I
• Makrokosmos II

Claude Debussy: (1862-1918)

• La Mer
• Nocturnes
• Prelude a l'apres-midi d'un faune

Morton Feldman: (1926-1987)

• Piano and String Quartet
• Structures

Other prominent composers of the 20th and 21st century:

• Thomas Ades
• Martin Bresnick
• Curtis Curtis-Smith
• Alberto Ginastera
• Pavel Haas
• Alan Hovhaness
• Leoš Janáček
• Ben Johnston
• Scott Joplin
• Gideon Klein
• Zoltan Kodaly
• Hans Krasa
• Gyorgy Kurtag
• Libby Larsen
• Tania Leon
• Zou Long
• Pauline Oliveros
• Carl Orff
• Harry Partch
• Stephen Paulus
• Astor Piazzolla
• Walter Piston
• Frank Proto
• Wolfgang Rihm
• Christopher Rouse
• Kaija Saariaho
• Giacinto Scelsi
• Paul Schoenfield
• Erwin Schulhoff
• Joseph Schwantner
• Bright Sheng
• John Philip Sousa
• Viktor Ullmann
• Heitor Villa-Lobos
• William Walton
• Kurt Weill
• Dan Welcher
• Chen Yi

George Gershwin: (1898-1937)

• Rhapsody in Blue
• Porgy and Bess
• An American in Paris

Philip Glass: (b. 1937)

• Glassworks
• Einstein on the Beach
• String Quartet No. 2 “Company”

Sofia Gubaidulina: (b. 1931)

• Offertorium (Concerto for Violin and Orchestra)
• Chaconne

Jennifer Higdon: (b. 1962)

• Zaka
• On a Wire
• Blue Cathedral
• Piano Trio

Paul Hindemith: (1895-1963)

• Cello Sonata Op. 25 No. 3
• Das  Marienleben, Op. 27
• Mathis der Maler

Lee Hyla: (1952-2014)

• String Quartet No. 4
• We Speak Etruscan
• Amnesia Variance

Charles Ives: (1874-1954)

• The Unanswered Question
• Central Park in the Dark
• Symphony No. 4
• The Cage
• Soliloquy

Aaron Jay Kernis (b. 1960)

• Colored Field
• String Quartet No. 2
• Musica Celestis

Erich Wolfgang Korngold: (1897-1957)

• Violin Concerto
• String Sextet Op. 10

Ladislav Kubik: (b. 1946)

• Piano Concerto No. 3
• String Quartet No. 1
• Trio for Violin, Cello and Piano

Gyorgy Ligeti: (1923-2006)

• Piano Etudes
  • Book 1 
  • Book 2
  • Book 3   
• Trio for Horn, Violin and Piano
• Lux Aeterna
• 6 Bagatelles

Witold Lutoslawski: (1913-1994)

• Concerto for Orchestra
• Livre pour orchestre
• Chain 2
• Partita for Violin and Orchestra

Olivier Messiaen: (1908-1992)

• Quatuor pour la fin du Temps (Quartet for the End of Time)
• Poemes pour mi
• La Nativité du Seigneur (The Birth of the Saviour)
• Turangalîla Symphonie

Darius Milhaud: (1892-1974)

• La creation du monde
• Le Boeuf sur le toit, Op. 58
• Saudades Do Brasil, Op. 67

Conlon Nancarrow: (1912-1997)

• Studies for Player Piano

Arvo Part: (b. 1935)

• Fratres
• Cantus in Memory of Benjamin Britten

Kryzstof Penderecki: (b. 1933)

• Symphony No. 7 “Seven Gates of Jerusalem”
• St. Luke Passion
• Threnody to the Victims of Hiroshima

Francis Poulenc: (1899-1963)

• Gloria
• Violin Sonata
• 3 movements perpetuels
• Les Biches
• Dialogues des Carmelites

Sergei Prokofiev: (1891-1953)

• Romeo and Juliet (Suite for Orchestra)
  • Suite 1
  • Suite 2
• The Love for Three Oranges (Suite for Orchestra)
• Symphony No. 2

Maurice Ravel:  (1875-1937)

• La Valse
• Gaspard de la nuit
• Bolero

Steve Reich: (b. 1936)

• Different Trains
• Piano Phase
• Vermont Counterpoint
• Clapping Music
• Saxophone Quartet

Terry Riley: (b. 1935)

• In C
• A Rainbow in Curved Air

Erik Satie: (1866-1925)

• Parade
• Socrate

Alfred Schnittke: (1934-1998)

• Concerto Grosso
• String Quartet No. 2
• Symphony No. 1

Arnold Schoenberg: (1874-1951)

• Five Pieces for Orchestra, Op. 16
• Pierrot Lunaire, op. 21
• Violin Concerto op. 36
• Piano Concerto, op. 42
• A Survivor from Warsaw, Op. 46

Gunther Schuller: (b. 1925)

• 7 Studies on Themes of Paul Klee

Ruth Crawford Seeger: (1901-1953)

• Violin Sonata
• Three Songs to Poems by Carl Sandburg
• Suite for Five Wind Instruments and Piano

Roger Sessions: (1896-1985)

• Symphony No. 2
• Divertimento for Orchestra

Dmitri Shostakovich: (1906-1975)

• Symphony No. 5
• String Quartet No. 8
• Piano Trio No. 2
• Lady Macbeth of the Mtsensk District, Op. 29
• Symphony No. 10

William Grant Still: (1895-1978)

• Symphony No. 1 “Afro-American”
• Symphony No. 2 “Song of a New Race”
• Troubled Island
• A Bayou Legend

Igor Stravinsky: (1882-1971)

• Le sacre du printemps (The Rite of Spring)
• Petrushka
• Symphony of Psalms

Karlheinz Stockhausen: (1928-2007)

• Kontakte
• Stimmung
• Klavierstucke V, Work No. 4
• Klavierstucke IX, Work No. 4

Virgil Thomson: (1896-1989)

• Four Saints in Three Acts
• The Mother of Us All
• 5 Songs from William Blake

Joan Tower: (b. 1938)

• Platinum Spirals
• Silver Ladders
• Sequoia
• Fanfare for the Uncommon Woman No. 1

Edgard Varese: (1883-1965)

• Integrals
• Density 21.5
• Ionisation
• Poeme Electronique

Anton Webern: (1883-1945)

• 5 Movements, op. 5
• 5 Pieces op. 10
• 6 Songs, op. 14
• Symphony, Op. 21

Ralph Vaughan Williams: (1872-1958)

• Along the Field
• Fantasia on a Theme by Thomas Tallis

La Monte Young: (b.1935)

• Compositions 1960
  • No. 7
• The Second Dream of the HighTension Line Step

Ellen Taaffe Zwilich: (b. 1939)

• Concerto Grosso 1985
• Clarinet Concerto
• Symphony No. 1