[9][10] The artwork is an edit of an illustration of a wolf of Southern States by English soldier, artist and naturalist Charles Hamilton Smith.

On June 10, a day before the No Gods No Masters release, Garbage performed "Wolves" on the Late Night with Seth Meyers show.

[13] A live performance of the song recorded at the Mates Rehearsal Studios in North Hollywood was sent to World Cafe[14] to promote the album while keeping social distance during the ongoing COVID-19 pandemic.

[15] The animated video makes heavy use of stop motion and rotoscoping and features two wolves reflecting the song's theme of duality.

James Rettig of Stereogum described the song as "a scorcher with some tangled-up guitars and a mewling Shirley Manson hook" whilst Mark Millar of XS Noize qualified it as "angularly powerful, hook-driven"[16] and Damian Jones of NME as "stomping" and "vitriolic.

"[18] In his 8/10 review for No Gods No Masters on Under the Radar, Andy Von Pip praised "Wolves" for being "classic Garbage demonstrating their innate ability to craft futuristic dystopian doom pop."

[19] Andrew Trendell was also positive in his review of the album for NME, calling the track "a devious little desert rock pop beast.