Later some sub-branches, like the Nerey (Nereus) were designed for coastal patrol by the KGB Border Troops.

Until 1977, the ships in the class were considered to be large anti-submarine warfare vessels.

Currently 2 vessels of the Nerey subclass are in service with the FSB Coast Guard and one was the flagship of the Ukrainian Navy (scuttled in 2022 to avoid capture).

The ship's unique features — the bow missile box, the stack and the angled mast, earned it a rap-like nickname among U. S. sailors that comes from their foreign ship silhouette identification training — "Hot dog pack, Smokestack, Knife in the Back, two Guns in the Back — Krivak.

On 12 October 2010, it was announced that the Yantar Shipyard at Kaliningrad had won a contract for construction of three new warships for the Russian Navy.