Everything I do feels like It's going to end up being in Radiohead.

Greenwood won the Radio 3 Listeners' Award at the 2006 BBC British Composer Awards for his piece "Popcorn Superhet Receiver". Greenwood composed the score for the 2007 film There Will Be Blood from director Paul Thomas Anderson. For a while Greenwood wore an arm brace due to a repetitive strain injury attributed to his "aggressive" way of playing the instrument often billed as "abusive guitar".

He is the younger brother of Radiohead bassist Colin Greenwood. Beyond his primary roles as Radiohead's lead guitarist and keyboardist Greenwood is a multi-instrumentalist and also plays viola harmonica glockenspiel ondes Martenot banjo and drums and works with computer-generated sounds and sampling; he is also a computer programmer and writes music software used by Radiohead.