Though it is one of the group's best known singles, it failed to make the top 40 in either the United Kingdom (only reaching No. 56) or the United States Billboard Hot 100. In the United States, the song also reached the eighth position on the Hot Dance Music/Maxi-Singles Sales chart, but failed to chart on the Hot 100 during its original 1986 release. However, a new mix included on the The Best of New Order was released in 1994 and finally made a brief appearance on the Billboard Hot 100 in the number 98 position in 1995. In Australia, the 1986 release was a sizable chart hit, reaching number 5 nationally and number 1 in Victoria.
The 12-inch version, remixed by Shep Pettibone, also appears on the compilation Substance and a second remix by Stephen Hague features on their Best Of album. The original album version appears on the 2005 compilation Singles.
The single mix features a cleaner sound with more electronics than the album version, notably the Fairlight CMI music workstation, the premier sampling keyboard workstation of the '80s, used to provide novel sounds, such as the orchestral hits that were so popular, but also to sequence the song. All instruments minus bass and voice were sequenced.
The music video, which was released in November, 1986, was directed by American artist Robert Longo. It prominently featured shots of a man and a woman in business suits flying through the air as though propelled by trampolines; this is based directly on Longo's "Men in the Cities" series of lithographs. The video also features a black and white cut-scene where Jodi Long and E. Max Frye are arguing about reincarnation, in which Long emphatically declares "I don't believe in reincarnation because I refuse to come back as a bug or as a rabbit!"
Australian band Frente! released an acoustic cover version of the song in 1994; it was the band's only major overseas success. This version was also the highest charting in the United States, peaking at 49 on the Billboard Hot 100.
It was remade into Chinese with the Cantonese version by Amanda Lee and the Mandarin version, by Sandy Lam, both under the title of "一個人 / Yī Gè Rén" ("Alone").
Brandon Flowers of The Killers, a band owing their name to New Order, has played "Bizarre Love Triangle" solo on piano at several of The Killers' concerts, as seen in widely circulated YouTube videos.
US editions mis-credit "Bizarre Dub Triangle" as "I Don't Care", reputedly due to a record company person contacting New Order's Manager Rob Gretton to ask what to name the mix as, Gretton is claimed to have said "I don't care"