Only two ships of this class exist; the original Kuznetsov, which is in Russian service, and the Varyag, which was sold to China, by Ukraine, which inherited the unfinished ship then building in a Ukrainian shipyard when the Soviet Union dissolved in 1991. The Varyag is still uncompleted, but the Kuznetsov entered service in 1995, after a decade of construction.
There was talk, in the Russian navy, of building more carriers. But this never got anywhere, and the naval aviation fans in the navy count themselves lucky that money has been allocated to do the "life extension" and upgrade refurbishment of the Kuznetsov.
The Russian navy is going to refurbish its only aircraft carrier, the Kuznetsov, so that it can remain in service until 2030. Originally the Kuznetsov class of four carriers were conceived of as 90,000 ton, nuclear powered ships, similar to American carriers (complete with steam catapults). Instead, because of the cost, and the complexity of modern (American style) carriers, the Russians were forced to scale back their goals, and ended up with two 65,000 ton (full load ) ships that lacked steam catapults, and used a ski jump type flight deck instead. Nuclear power was dropped, but the Kuznetsov class was still a formidable design. The thousand foot long carrier normally carries a dozen navalized Su-27s (called Su-33s), 14 Ka-27PL anti-submarine helicopters, two electronic warfare helicopters and two search and rescue helicopters. Alternatively, the ship can carry up to 36 Su-33s and sixteen helicopters. The ship carries 2,500 tons of aviation fuel, allowing it to generate 500-1,000 aircraft and helicopter sorties. Crew size is 2,500 (or 3,000 with a full aircraft load.)