The song was released as the first single from In Rainbows on 14 January 2008, following the album's 'standard' physical release on December 31, 2007.

The song was previously known as 'Open Pick', a title it was given provisionally when it was performed during Radiohead's 2006 tour.

The song has spent several weeks as one of the 100-most-played songs on US modern rock radio, so far peaking at #69, receiving more support than any other In Rainbows song with the exception of 'Bodysnatchers', which has hit #8 on the Billboard Modern Rock Chart, and House of Cards which has peaked at #48.

The track reached #30 in the UK singles chart on its first week of release, their lowest ranking chart entry since 'Lucky' in 1995. However, 'Jigsaw' was the first Radiohead single since the band's inception not to be released through EMI-controlled Parlophone, their former major record label. The single was instead released in the UK by independent label XL Records.

Time magazine named 'Jigsaw Falling Into Place' one of The 10 Best Songs of 2007, ranking it at #5.

Writer Josh Tyrangiel praised the song's 'tightness' whose rise in intensity he likened to a three-act play, and described the song as 'a journey through flirtation, consummation and regret that gets about as close as you can to summing up a doomed relationship in four minutes'.

The black-and-white music video features the five members of Radiohead playing the song in a room with footage taken using 'head cams'. The video was directed by Adam Buxton and Garth Jennings. It was uploaded to the band's YouTube page on 28 November 2007. It is the first Radiohead video to feature the whole band since the video for the band's 2003 '2 + 2 = 5' single.