Soundgarden performed this entreaty to do whatever moves you on The Tonight Show with Jimmy Fallon on June 3, 2014. "'My Wave' was either the next to last or the last song that we wrote for Superunknown in its entirety," lead singer Chris Cornell explained on the show. "We were just rehearsing, and I don't know what we were rehearsing for... we were about to leave, we were just about to grab our car keys, and we started playing the riff and then everybody immediately started playing the song."
Chris Cornell credits a 1979 song called "My Beach" by the Malibu band Surf Punks for inspiring the line "Keep it off my wave." In the Surf Punks song they sing, "My beach, my chicks, my waves... go home." That song is about the territorial nature of surfers.
Released as the fourth single from Superunknown, the song peaked at #11 on the Billboard Mainstream Rock Tracks chart and #18 on the Billboard Modern Rock Tracks chart. It also reached #50 on the Australian singles chart, #46 in New Zealand and #66 in Canada.
The song appeared in the trailer for the 1994 film, The Endless Summer II.
The music video was co-directed by bassist Ben Shepherd's brother, Henry Shepherd.