Czukay was born in the Free City of Danzig. Czukay co-founded krautrock group Can in 1968. He played bass guitar and performed most of the recording and engineering for the group. He left Can in 1977 a few years before the group's official breakup, and was replaced by bassist, Rosko Gee, of the British band, Traffic. After his departure from Can, Czukay recorded some notable early ambient albums. His trademarks became the use of shortwave radio sounds and his early pioneering of sampling, in those days involving the painstaking cutting and splicing of magnetic tapes. He would tape-record various sounds and snippets from shortwave and incorporate them into his compositions. He also used shortwave as a live, interactive musical instrument, a method of composition he termed radio painting.