Robert Andre Glasper was born on April 5, 1978, in Houston, Texas. His mother, Kim Yvette Glasper, sang jazz and blues professionally and took him along to her club dates, and she was music director at the East Wind Baptist Church, where he first played in public. He went on to play services at Baptist, Catholic and Seventh-day Adventist churches and has said that the way he hears harmony, and his habit of blending gospel chords into jazz, began there. He attended Elkins High School in Missouri City, Texas, and Houston's High School for the Performing and Visual Arts, played with the Texas Southern University jazz band in tenth grade, and was a student at the second Vail Jazz Workshop in 1997. He then moved to New York for the New School for Jazz and Contemporary Music, where he met the singer Bilal; the two began performing and recording together, which led to work with the neo-soul and hip-hop circle around Jill Scott, The Roots and J Dilla.

While still a student he began touring as a sideman with Christian McBride, the trumpeter Terence Blanchard and Roy Hargrove, and he became music director for the rapper Yasiin Bey, then performing as Mos Def. His first album as a leader, Mood, was recorded in 2002 and released in 2004 by Fresh Sound New Talent; it is mostly a piano trio session with bassist Bob Hurst and drummer Damion Reid, with Bilal and the saxophonists John Ellis and Marcus Strickland on some tracks. His Blue Note debut, Canvas, was recorded over four days in May 2005 at Systems II Studios in Brooklyn and released on October 4, 2005, with bassist Vicente Archer and Reid forming the trio he would use for years and Mark Turner on tenor saxophone for some tracks; the final track opens with a live recording of his mother singing. In My Element (2007) followed with the same trio and included pieces for his mother and for J Dilla, along with a medley that moves from Herbie Hancock's "Maiden Voyage" into Radiohead's "Everything in Its Right Place."

Double Booked (2009) split the program between the acoustic trio and an electric group, the Robert Glasper Experiment, with bassist Derrick Hodge, saxophonist and vocoder player Casey Benjamin and drummer Chris Dave; Bilal and Yasiin Bey are among the guests, and "All Matter," with Bilal, received a Grammy nomination for Best Urban/Alternative Performance. The Experiment took center stage on Black Radio, released in February 2012 with guests including Lupe Fiasco, Bilal, Lalah Hathaway, Erykah Badu and Yasiin Bey. It reached number 15 on the Billboard 200 and won the Grammy Award for Best R&B Album at the 2013 ceremony. Black Radio 2 followed in October 2013 with Mark Colenburg replacing Dave on drums and guests including Common, Brandy, Jill Scott, Norah Jones, Snoop Dogg and Lupe Fiasco; its version of Stevie Wonder's "Jesus Children of America," with Lalah Hathaway and Malcolm-Jamal Warner, won the Grammy for Best Traditional R&B Performance.

He returned to the acoustic trio for Covered, recorded live at Capitol Studios in Hollywood on December 2 and 3, 2014, with Archer and Reid, and released on June 16, 2015; it was nominated for the Grammy for Best Jazz Instrumental Album. That year he also played keyboards on Kendrick Lamar's To Pimp a Butterfly, co-produced the tribute album Nina Revisited... A Tribute to Nina Simone with Lauryn Hill, and produced, composed and arranged music for the Miles Davis film Miles Ahead, whose soundtrack won the 2017 Grammy for Best Compilation Soundtrack for Visual Media. Everything's Beautiful (May 27, 2016, Columbia and Legacy) recast Davis recordings with guests including Stevie Wonder, Erykah Badu, Laura Mvula, Ledisi and John Scofield, and ArtScience (September 16, 2016) brought back the Experiment. In 2017 he assembled the Blue Note All-Stars, with trumpeter Ambrose Akinmusire, saxophonist Marcus Strickland, guitarist Lionel Loueke, drummer Kendrick Scott and Hodge, for Our Point of View, co-produced by Don Was, with Herbie Hancock and Wayne Shorter sitting in on one track.

Two new groups appeared in 2018. R+R=NOW, with Terrace Martin, Hodge, Taylor McFerrin, trumpeter Christian Scott aTunde Adjuah and Justin Tyson, released Collagically Speaking on Blue Note on June 15, 2018, and August Greene paired Glasper with the rapper Common and the drummer and producer Karriem Riggins. Glasper and Riggins both worked on Common's Black America Again (2016), and "A Letter to the Free," the song Glasper produced and wrote with Common and Riggins for Ava DuVernay's documentary 13th, won the 2017 Primetime Emmy Award for Outstanding Original Music and Lyrics. In October 2018 he began an annual month-long October residency at the Blue Note Jazz Club in New York, now known as Robtober. His next record, Fuck Yo Feelings (October 3, 2019), was his first for Loma Vista Recordings, made in a two-day session with musician friends who dropped by the studio; that year he was also artist in residence at the North Sea Jazz Festival and the Kennedy Center. He scored the documentary The Apollo and the film The Photograph (released February 14, 2020), and in 2020 formed the group Dinner Party with Terrace Martin, Kamasi Washington and the producer 9th Wonder. His single "Better Than I Imagined," with H.E.R. and Meshell Ndegeocello, won the Grammy for Best R&B Song, and Black Radio III (February 25, 2022) won Best R&B Album at the 2023 ceremony.

Let Go (June 7, 2024) first appeared through Apple Music; Code Derivation (August 28, 2024) pairs band takes with versions reworked by producers including Hi-Tek, Black Milk, Karriem Riggins, Taylor McFerrin and his son Riley; and Keys to the City Volume One (October 11, 2024) collects nine performances from Robtober with guests including Black Thought, Norah Jones, Thundercat, Meshell Ndegeocello and Esperanza Spalding. Keys to the City was nominated for Best Alternative Jazz Album at the 2026 Grammy Awards, which went to Nate Smith's Live-Action. In 2026 Glasper is creative ambassador of Blue Note London, the club's first UK venue, and played its opening night in September; his eighth Robtober at the Blue Note Jazz Club in New York was scheduled to run from October 1 to November 1, 2026.

Glasper plays with an acoustic jazz pianist's harmonic vocabulary and a producer's ear for groove. He traces his sense of harmony to church music and has said that A Tribe Called Quest drew him to hip-hop, and he regards Miles Davis as the model for a musician who keeps reflecting the sound of his own time; Everything's Beautiful and the Miles Ahead score are the plainest statements of that debt, and his early records already covered Herbie Hancock's "Maiden Voyage" and "Riot." His output runs on two tracks. The acoustic trio plays originals, standards and piano arrangements of songs by Radiohead, Joni Mitchell, Kendrick Lamar and Bilal (Covered), while the Experiment works with Fender Rhodes, vocoder and a rotating cast of singers and rappers, and has also reworked Nirvana's "Smells Like Teen Spirit." Critics have reacted to that range in different ways. Rolling Stone called Black Radio a blueprint for what comes next, and four of his five Grammy wins are in R&B categories, the fifth being for a film soundtrack. Jazz institutions have claimed him as well: in DownBeat's 2013 Critics Poll he won the Keyboard category, the Beyond category with the Experiment, and the Rising Star Composer and Rising Star Producer categories; Covered was nominated for Best Jazz Instrumental Album, Keys to the City Volume One for Best Alternative Jazz Album, and he has held artist-in-residence posts at the North Sea Jazz Festival, the London Jazz Festival, the Kennedy Center, Carnegie Hall and the Blue Note Jazz Club. His public profile now rests as much on production, film scoring and collaboration with rappers and singers as on his own records, but the piano trio remains his base, and his annual Blue Note residency keeps both sides of the work in front of the same audience.