Sensuuri's story started in summer 1978, when young and prospective musicians Pepe Lempinen and Costello Hautamäki met in a confirmation class, and decided to form a band. Later Kari Larmila, Pepe's friend from school, joined in to play bass, and Pasi Pakarinen joined to play drums. Soon Kari was replaced with Jaska Oinonen, thus forming the quartet as Sensuuri is best remembered.
In fall 1978 Epe Helenius happended to see them play live in Safety Pins Club, and he immediately offered them a chance to record a single for Poko Rekords. The single Kirjoitan seinään was released in early 1979. The single and increased gigging brought more attention, so it was time to consider recording a full album. The band started practising new material, and as a result Hulinaa album, produced by Pantse Syrjä, was released in summer 1979.
The album was followed by singles Kaupunki nukkuu and Hengissä läpi Helsingin. In 1980 Sensuuri recorded the song Vaarallinen rakkaus for the Hellää terroria korville EP, in the intention to promote a fortcoming second album. However, things didn't work out as planned: Jaska Oinonen left the band, soon followed by Pepe Lempinen.
Costello and Pasi continued with variable lineups. With the lineup Costello-guitar and vocals, Matti Hamppunen-bass, Vesa Kujala-keyboards and Pasi Pakarinen-drums, Sensuuri released the single Goodnight N.Y.C. in 1981, and recorded songs for an album. At the same time Pasi had to perform his compulsory military service, and Costello joinded Popeda. This caused Sensuuri to break up for good, and Pasi and Costello saw no point in releasing the new album, since the band was no more.
After quitting Sensuuri Jaska joined Kohu-63. Costello made a career in Popeda. Pepe recorded a solo single, sang in various bands, and later quit the music scene. Pasi Pakarinen has played in several bands, including Pojat.