Robert Gillespie (born 22 June 1961) is a Scottish musician, singer-songwriter, and multi-instrumentalist. He is the lead singer, founding member, primary lyricist, and sole continuous member of the alternative rock band Primal Scream. He was the drummer for The Jesus and Mary Chain in the mid-1980s, leaving after the release of the band's debut album Psychocandy, and was once the bassist for The Wake.

In October 2021, Gillespie published his memoir Tenement Kid.