The Soviet Navy lives, or at least two of its largest ships, both of them aircraft carriers. Russia, the core (and half the population) of the old Soviet Union spent several decades creating the world's second largest navy. By the end (the 1980s) they had half a dozen aircraft carriers in service or under construction. Only three of those carriers are still around. One is operated by Russia, the other two have been sold off and rebuilt by their new owners. China recently commissioned the former Russian carrier Varyag as the Liaoning. India also rebuilt a Russian carrier (Gorshkov) as Vikramaditya.
These two Russian carriers are quite different, the Gorshkov being smaller (45,000 ton) and basically a large cruiser (with hundreds of anti-aircraft and anti-ship missiles) along with some vertical take-off (V/STOL) jets and helicopters. These jets were the Yak-38 "Forger". The Forger was better than the original AV-8 Harrier but not as capable as the later AV-8B. It lacked internal cannon (compared to two 30 millimeter in the AV-8A Sea Harriers of India and the UK or a 25 millimeter Gatling gun in the U.S. AV-8B series) and had a lower payload (3.5 tons versus six tons on the AV-8B series). To make matters worse for the Yak-38Forger, it also had less range (200-360 kilometers on a typical mission as opposed to 1,100 kilometers for the AV-8B). A replacement aircraft, the Yak-141, died with the end of the Cold War, and while it was faster than the AV-8B series, it was clearly not a match for the AV-8B overall. India has Russia rebuild the Gorshkov as a conventional carrier, without all the missiles and vertical take-off jets. The Vikramaditya will operate 16 MiG-29K jets and twelve helicopters. Gorshkov was the fourth Kiev class "cruiser-carrier". The first one entered service in 1975, and the last one in 1987. Based on the experience with the Kievs the decision was made to build the larger Kuznetsovs.
Liaoning is one of the two Kuznetsov class carriers that Russia began building in the 1980s. Originally the Kuznetsovs were to be 90,000 ton nuclear powered ships, similar to American carriers (complete with steam catapults). Instead, because of the high cost and the complexity of modern (American style) carriers, the Russians were forced to scale back their plans and ended up with 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 Kuznetsovs were still a formidable design.
The Kuznetsovs were designed to carry a dozen navalized Su-27s (called Su-33s), 14 Ka-27PL anti-submarine helicopters, two electronic warfare helicopters, and two search and rescue helicopters. But the ship could carry as many as 36 Su-33s and sixteen helicopters. The Kuznetsovs carry 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). While the original Kuznetsov is in Russian service, the second ship, the Varyag, was launched but not completed and work stopped in 1992. The Chinese bought the unfinished carrier in 1998, towed it to China and spent over a decade completing it as the Liaoning.