And Their Refinement of the Decline is the seventh and final studio album by Stars of the Lid, which was released by Kranky in April 2007. The album was Kranky's 100th release, and was issued as a double CD and as a triple vinyl LP set (featuring alternate artwork). And Their Refinement of the Decline features minimal, droning compositions of varied length created from treated guitar, horn, piano, and other classical instruments.

The track "Dopamine Clouds Over Craven Cottage" refers to Craven Cottage in London, the home stadium of English football club, Fulham F.C. At the time of the album's release, their captain was ex-United States soccer international Brian McBride, who shares the same name as Brian McBride from Stars of the Lid. The track "Don't Bother They're Here" uses the melody of Stephen Sondheim's 1973 song "Send in the Clowns".

In December 2007, American webzine Somewhere Cold ranked And Their Refinement of the Decline No. 5 on their 2007 Somewhere Cold Awards Hall of Fame.