Neu! 4 was recorded and mixed between October 1985 and April 1986 at Grundfunk Studio and Dinerland-Lilienthal Studio in Düsseldorf, Germany, and Michael Rother Studio in Forst, Germany. This was the first time Rother and Klaus Dinger had entered a studio together since 1975. However, the sessions were not completed and the planned album was abandoned.
During the 1990s, the first three Neu! albums were available on CD on Germanofon Records, a dubious label allegedly based in Luxembourg who specialized in unauthorized and illegal reissues (bootlegs) of otherwise unavailable krautrock albums. Germanofon managed to get a number of their releases, including the three Neu! albums, into mainstream distribution. According to Rother's account, Dinger released Neu! 4 "in an act of despair, so he says" in late 1995 as a response to the bootlegs, which Dinger railed against in the liner notes. Neu! 4 was issued by the Japanese label Captain Trip Records, without Rother's input, knowledge or consent. He only learned what had happened in a telegram congratulating him on the release of the album. Rother, writing in March 2007, described this experience as "a rather painful disaster between Klaus Dinger and myself".
The release of Neu! 4 exacerbated the disagreements between Rother and Dinger, which prevented an official CD release of the three classic Neu! albums until 2001. The 2000 agreement between Rother and Dinger which led to the CD releases on Astralwerks in the U.S. and Grönland Records in the UK called for Neu! 4 to be recalled, and it has been out of print since then.
Despite Rother's continued objection to Dinger's original decision to release Neu! 4 and his oft stated opinion "that [Neu! 4] isn't a legal/real Neu! album", Rother had no objection to fans buying the CD secondhand and would always leave open the possibility that Neu! 4 could be reissued legally with his consent in the future. Rother and Dinger did attempt to negotiate such a release after the official reissue of the first three albums. In March 2007, Rother termed the failure to reach such an agreement "unfortunate". With Dinger's death in 2008, such an agreement seemed unlikely.
In early 2010, Rother announced that he had arrived at an agreement arranged with Dinger's heir, Miki Yui, and had completely remastered the album from original multitrack and master tapes to produce Neu! '86, which he termed "our fourth studio album".
The new album shared several tracks in common with the original release, but has a few new or remixed tracks. Critics have argued that the new version seems overproduced.