The music video, released on April 11, 2008, features scenes of a young woman traveling alone to various places around the world, interspersed with the band performing in an industrial freezer room.

The song's lyrics depict a one-sided obsessive relationship from the point of view of the pursuer, who implores the object of his affection that she needs to "spend some time" with him so that he might "possess [her] heart.

[4]The song is written in the key of D, but the main motif continually switches modes from major to minor as the chord goes from D to F with a moderate tempo of 134 beats per minute.

[6][8] Gibbard credited Nick Harmer's bass line with being integral to the song, noting inspiration from bassists Eric Avery and Simon Gallup.

James Montgomery of MTV News said of the song, "there are moments on Stairs that stop you dead in your tracks, send shivers up your spine and make you go 'Whoa'... like the first four-and-a-half minutes of 'I Will Possess Your Heart,' a propulsive whirl of stalking bass line, spindly guitars and stabbing piano.

"[8] Will Hermes noted in Rolling Stone that the sense of menace in the song was "playing against type for a guy with one of rock's purest voices—a vibrato-less, bell-clear high tenor whose choirboy quality only throws the darkness here into relief.

"[10] Blender's Jonah Weiner concurred, stating "it's a pleasant surprise to hear Gibbard inhabit such a self-consciously creepy role, rather than play the occasionally errant, essentially good-hearted boyfriend who soft-shoes through so many of his tales.

[14] The music video features scenes of a young woman traveling alone to various places around the world, interspersed with the band performing in an industrial freezer room.

The video was shot in New York City, London, Paris, Frankfurt, Tokyo, Hokkaido, Tunis, Carthage, Bangkok, Siem Reap, and Phnom Penh.

[16] Stewart-Ahn selected Shawn Kim to direct the shots of the band, and although they never met in person they established visual motifs to unite their respective parts of the video.

[15] Unlike Stewart-Ahn's section of the video, Kim used a professional Arriflex 435 camera and Panavision E-Series lenses, which he felt added to the coldness of the image.