The class was a follow-up to the Kara-class cruiser, which the Soviet Navy typed as a Large Anti-submarine Ship (Russ.

A fourth vessel was launched, but final construction remains incomplete, and the ship has not been commissioned into service.

After the dissolution of the Soviet Union, the three finished ships commenced service in the Russian Navy, while the uncompleted fourth vessel, renamed Ukraina, had its ownership transferred to Ukraine.

[7] The Russian Navy had plans to extensively upgrade all of their Slava-class vessels during the 2010s; completing work on Ukraina may have served as a test-bed for this.

One of the vessels, Moskva, sank in the Black Sea on 13 April 2022 following an explosion during the Russian invasion of Ukraine.