The group is composed of guitarist-singer Mansur Zennelli, guitarist Michael Barrett, drummer Salvatore Aidone, bassist Duncan Millar and lead singer Christopher de Cinque.

To date they have released one extended-play and three full-length studio albums: The Penance and the Patience (2008), First Temple (2009), Pink Lemonade (2014), and Soft Hell (2023) respectively.

[4] They went to extreme lengths to record The Penance and the Patience: the band spent three to four months straight writing or doing preproduction, as well as quitting jobs to go on tour.

[9] The band used a wide array of instruments to achieve a fuller sound, including double bass, trumpet, trombone and a dobro guitar with strings that were 20 years old.

Band members Michael Barrett, Mansur Zennelli, and Christopher de Cinque worked as session musicians on the album A Dream Is a Question You Don't Know How to Answer by Jonny Craig.

[17] In 2017, the band returned from writing sessions to play shows with Protest The Hero, before announcing they would premiere new material live on tour with Danish dream pop group MEW in September.

In September, the band were announced as the support for The Dillinger Escape Plan's final ever Australian tour at their sold-out shows in Melbourne, Sydney and Brisbane.

2018 saw Closure in Moscow return to North America for the first time in eight years, supporting Protest The Hero during March and April, as well as playing their own headline dates in New York, Pennsylvania and Texas where they performed First Temple in full.

[20] Similarities with Saosin have also been noted in a live review in Sydney street press Drum Media of a show with label mates Fifty Sixx.

The band has also been compared to other experimental and progressive rock acts The Mars Volta and Circa Survive by music website Absolute Punk.

[6] However, the rise of previous bands with similar styles, such as Coheed and Cambria, has altered the meaning of avant-garde, which describes "those artists, writers, or musicians, whose techniques and ideas are in advance of those generally accepted.