Einstürzende Neubauten's earliest recordings are mostly unstructured, free-form noise issued on various cassettes and singles, including their first single "Fuer den Untergang," the 1981 EP Schwarz, and the 1982 album Kollaps. Some of these recordings are compiled on the Strategies Against Architecture '80-'83 collection, with live shows on the cassette-only 2x4. Bartel and Gut were replaced by ex-Abwräts member F.M. Einheit (who served as Neubauten's chief machinery operator) in 1983, when guitarist and electronics expert Alexander Hacke and Abwräts bassist Mark Chung also joined. A tour of England opening for the Birthday Party resulted in a contract with Some Bizarre Records, which released the slightly more structured Zeichnungen des Patienten O.T., as well as consternation from club owners and journalists over Neubauten's stage demolitions and frequent ensuing violence.

When Nick Cave left the Birthday Party and formed his backing band the Bad Seeds, Bargeld became the guitarist and toured and recorded with Cave over most of the decade. He remained with Neubauten, however, which released Halber Mensch in 1986, showcasing its wider range of expression. The group disbanded briefly but soon re-formed, and has released albums off and on since then for Elektra, signing to Trent Reznor's Nothing label for 1998's Ende Neu. While Bargeld remained a Bad Seed, Van Borsig and Hacke contributed to the remainder of the Birthday Party's recordings as Crime & the City Solution. In May 2000, Einstürzende Neubauten released the full-length Silence Is Sexy on Mute Records. Two years later, they announced they were no longer interested in working with a traditional label and that their next recording would be made with the help of supporters. These supporters would pay a fee, receive exclusive material, and help fund the next official album.

Despite their best intentions, Einstürzende Neubauten released their 2004 album, Perpetuum Mobile, on Mute. The releases for supporters that appeared over the next few years helped fund the official album Alles Wieder Offen, which was released on the band's own label in 2007. Elektra reissued both Strategies Against Architecture compilations on CD, and another supporter album, Einstürzende Neubauten, arrived in mid-2007. The Jewels arrived in 2008. It was compiled from a series of single-track digital downloads the band offered via its website one at a time using a game called DAVE, where deliberate and enigmatic instructions were inscribed on cards each member drew and generated ideas from -- without telling one another what their cards were inscribed with. They were then used to construct and complete tracks within a day or two. In 2010, Mute released the compilation Strategies Against Architecture, Vol. 4, and the album Kollaps was remastered and reissued by Potomak.