The Velvet Underground was an American rock band formed in New York City in 1964. The New York Times wrote that the Velvet Underground was "arguably the most influential American rock band of our time". Though their integration of rock and the avant-garde earned them little commercial success during their initial nine-year run, they are now widely regarded as one of the most influential bands in rock music, as well as underground, experimental, and alternative music. Their provocative subject matter and experimentation were instrumental in the development of punk rock, new wave and other genres.

The group performed under several names before settling on the Velvet Underground in 1965, taken from the title of a 1963 book on atypical sexual behavior. Its classic lineup consisted of singer and guitarist Lou Reed, Welsh multi-instrumentalist John Cale, guitarist Sterling Morrison, and percussionist Moe Tucker. In 1966, pop artist Andy Warhol became their official manager. They served as the house band at Warhol's studio, The Factory, and performed with his traveling multimedia show, Exploding Plastic Inevitable, from 1966 to 1967. Their debut album, The Velvet Underground & Nico, featuring the German singer and model Nico, was released in 1967 to critical indifference and poor sales, although it has since been hailed as one of the greatest albums in music history.

The band released their second album, the abrasive White Light/White Heat, in 1968, after which Cale was replaced with Doug Yule. They then released two more accessible albums, The Velvet Underground (1969) and Loaded (1970), but neither performed to the expectations of record labels or de facto group leader Reed. In the early 1970s, all but Yule left the band for various reasons. A final album was released under the Velvet Underground name in 1973, Squeeze, recorded mostly by Yule with Ian Paice of Deep Purple and other session musicians in London. The Velvet Underground dissolved shortly after.

The former band members collaborated on each other's solo work throughout the 1970s and 1980s, and an album of long lost recordings of original songs, VU, was released in 1985. Reed, Cale, Tucker and Morrison reunited for a series of well-received shows in 1993, and released a live album from the tour, Live MCMXCIII, later that year. After Morrison's death in 1995, the remaining members performed at their Rock and Roll Hall of Fame induction in 1996. In 2004, the Velvet Underground were ranked number 19 on Rolling Stone's list of the "100 Greatest Artists of All Time". Following Reed's death in 2013, the group received the Grammy Lifetime Achievement Award in 2017.

The foundations for what would become the Velvet Underground were laid in late 1964. Singer-songwriter and guitarist Lou Reed had performed with a few short-lived garage bands and had worked as a songwriter for Pickwick Records (Reed described his tenure there as being "a poor man's Carole King"). Reed met John Cale, a Welshman who had moved to the United States to study classical music upon securing a Leonard Bernstein scholarship. Cale had worked with experimental composers John Cage, Cornelius Cardew and La Monte Young, and had performed with Young's Theatre of Eternal Music, though was also interested in rock music. Young's use of extended drones would be a profound influence on the band's early sound. Cale was pleasantly surprised to discover that Reed's experimentalist tendencies were similar to his own: Reed sometimes used alternative guitar tunings to create a droning sound. The pair rehearsed and performed together; their partnership and shared interests built the path towards what would later become the Velvet Underground.

Reed's first group with Cale was the Primitives, a short-lived group assembled to issue budget-priced recordings and support an anti-dance single written by Reed, "The Ostrich", to which Cale added a viola passage. Reed and Cale recruited Sterling Morrison—a college classmate of Reed's at Syracuse University—as a replacement for Walter De Maria, who had been a third member of the Primitives. Reed and Morrison both played guitars, Cale played viola, keyboards and bass and Angus MacLise joined on percussion to complete the initial four-member unit. This quartet was first called the Warlocks, then the Falling Spikes. The Velvet Underground by Michael Leigh was a contemporary mass market paperback about the secret sexual subculture of the early 1960s; Cale's friend and Dream Syndicate associate Tony Conrad showed it to the group, and MacLise made a suggestion to adopt the title as the band's name. According to Reed and Morrison, the group liked the name, considering it evocative of "underground cinema", and fitting, as Reed had already written "Venus in Furs", a song inspired by Leopold von Sacher-Masoch's book of the same name, which dealt with masochism. The band immediately and unanimously adopted "The Velvet Underground" as its new name in November 1965.

The newly named Velvet Underground rehearsed and performed in New York City. Their music was generally much more relaxed than it would later become: Cale described this era as reminiscent of beat poetry, with MacLise playing gentle "pitter and patter rhythms behind the drone".

In July 1965, Reed, Cale and Morrison recorded a demo tape at their Ludlow Street loft without MacLise, because he refused to be tied down to a schedule and would turn up to band practice sessions only when he wanted. When he briefly returned to Britain, Cale attempted to give a copy of the tape to Marianne Faithfull, hoping she would pass it on to Mick Jagger, lead singer of the Rolling Stones. Nothing ever came of this, but the demo was eventually released on the 1995 box set Peel Slowly and See.