Shuman was born in Brooklyn, New York and went to Abraham Lincoln High School and then studied music at the New York Conservatory. He became a fan of R&B music and after he met Doc Pomus the two teamed up to compose for Aldon Music at offices in New York City's Brill Building. Their songwriting collaboration saw Pomus write the lyrics and Shuman the melody, although occasionally they worked on both. Their compositions would be recorded by artists such as Dion, Andy Williams, Bobby Darin, Fabian, The Drifters, and Elvis Presley, among others. Their most famous songs include "A Teenager in Love", "Turn Me Loose", "This Magic Moment", "Save The Last Dance For Me", "Little Sister", "Can't Get Used to Losing You", "(Marie's the Name)His Latest Flame" and "Viva Las Vegas".
Pomus often drew on life events which inspired his creativity. It was after a break-up with his girlfriend that Pomus, who had been driving in his car, was struck in awe by the sounds of the car horns blaring amidst his thoughts. Arriving at the studio, Pomus attempted to assimilate the sound of the horns and penned an introduction to a piece he initially titled "A Crowded Avenue". Later, the work progressed with Shuman, who helped finalize the draft. A chorus was added and the name of the song was changed to "Can't Get Used to Losing You", which became one of the biggest hits for Andy Williams in 1963.
With the advent of the British invasion, they moved to London where they penned songs for a number of British musicians. After the partnership with Doc Pomus ended in 1965, Shuman moved to Paris, France where he wrote songs for the French rocker Johnny Hallyday and embarked on his own recording career. He also found time to write a couple of hits in the UK (including one for The Small Faces written with Kenny Lynch), as well as a musical, Budgie (lyrics by Don Black).
In 1968, Shuman adapted the French lyrics of songs by the Belgian composer Jacques Brel used as the basis of the highly successful off-Broadway production Jacques Brel is Alive and Well and Living in Paris. He appeared in both the stage revue and the 1975 film adaptation.
Shuman was elected to the Songwriters Hall of Fame in 1992. He also worked occasionally as an actor, notably appearing with Jodie Foster in The Little Girl Who Lives Down the Lane.
He died (from complications due to a liver operation) at the age of 54.
