It is her first album recorded entirely as a solo act, following 2014's Trouble in Paradise, on which former member Ben Langmaid still contributed to a number of songs.

Supervision was preceded by three singles: "International Woman of Leisure", "Gullible Fool", and "Automatic Driver", but none of them made an impact on the charts.

In spring 2015, Jackson announced that she had begun working on the third La Roux album and that she wanted it to be "futuristic and innovative".

[3] In August 2015, Elly shared that she was already working with "a lot" of material and that she wanted the new album to be "even warmer [than the previous record], very energetic and quite loose".

[12][13] The new material was created in Jackson's own studio at her house in South London's Brixton/Herne Hill area and each song reportedly took five hours to record.

[17] Supervision is a synthpop[18] and dance-pop[19][20] album that incorporates funk,[21] reggae,[22][23] disco,[24] house,[25] britpop,[26] and sophisti-pop.

She said that it "encapsulates a cycle of a life, (...) describes the feeling of being overly trusting, and living under the assumption that you shouldn't need to protect yourself if you are nice to people.

[It] covers several times in my life when I've been bullied and it's taken me totally by surprise, and then moves into the build of the inner fortress to a place of safety and joy".

[41] In mid-October 2019, the album's title, tracklist and release date emerged on a number of online music retailers,[42][43] although no official announcement had been made.

On 30 October 2019, Jackson posted a teaser of the upcoming lead single "International Woman of Leisure", which was released the following day as her first musical output in over five years.

[46] The album was released independently on Jackson's own Supercolour Records on 7 February 2020, licensed to distributing company Believe, after she and her previous label Polydor parted ways in 2015.

[7] Supervision was released in multiple formats and was accompanied by a special limited edition magazine which Jackson dubbed "fantazine".

[28][33] The critics tended to select "International Woman of Leisure",[58][59] "Gullible Fool",[32][60] "Do You Feel" and "Automatic Driver"[51] as the album's highlights.

[57][59] In a more neutral review, Ben Devlin of musicOMH reflected that "Supervision is at times frustrating [but] also contains some of La Roux's best music to date".

[21] Some reviewers described the record as "repetitive"[51] and "samey",[33][34] with "never enough distinction between the album's tracks"[29] which they found sound too similar to each other.