This was something that Beck originally recorded in the late 2000s when was producing and writing for some other artists, but the song never got used. He told Q magazine: "I was recording a bunch of orchestral things for another record that was much more... challenging (laughs). 'Wave' was the calm at the eye of the storm. After the record was shelved, 'Wave' became part of Morning Phase."
The song became the center piece of Morning Phase. Beck told NPR: "I just had it sitting around for a long time, and when I played it for people it always got a reaction, do I started to put together songs that felt like they could go with that song and build around that. That was always the center of the record."
Beck's father, David Campbell, reprised his role on several other of his son's albums in handling the song's brass and string arrangements.
Beck debuted the song during a performance in LA's Walt Disney Concert Hall on November 24, 2013.
Beck suffered a spinal injury in 2008, which left him in a great deal of pain for a number of years and unable to pick up his guitar. Asked by Clash magazine if this song ties into that bleak period, he replied: "I sat down to write, and that came out. It's one of those things where… Well, maybe when you sit down with an intention to write something, but it's never exactly what comes out. And I don't think I have a choice in that matter! You can only hear a song like that… I just have to accept that is what came out, and it represents something."
The "isolation" Beck sings about does appear to be referring to the pain hitting him like a wave leaving him feeling alienated from normal life.