So limiting this to the 20 year rule, and thus 1997 first off with only brief references to events and trends past it. We can actually though talk a good deal about Soviet carrier efforts, which obviously play a huge part in how Russian and PLAN Naval Aviation evolved.

Simply put, from their origins to today an aircraft carrier is a tool of power projection. It allows you to take a piece of ocean that couldn't be used as an airbase and suddenly you have a fully functional one with up to +75 aircraft ready to go and which can be somewhere 100's of miles away tomorrow. It is a tool to enable expeditionary warfare and a sustained presence beyond the limits of land based aircraft for the power that has one. From Imperial Japan, to the United States and Great Britain, to the French, to other minor carrier nations, it has always been about building the ability to go someplace else and attack there using your big moving runway.

To avoid too deep an overview we can then suffice to say that they were crucial to Allied victory in WW2, very important in US efforts in SE Asia in the Cold War and elsewhere, and factored heavily into plans for a NATO/Warsaw Pact confrontation. And carriers through the years have done numerous different missions, often all at the same time. They can first and foremost attack other naval assets(ships, planes, subs), can attack ground targets and support landings, and can protect sea lanes of communication from enemy forces. All 3 have been key over the years from the drive across the Pacific and Battle of the Atlantic, to supporting fighting in Korea, Vietnam, and in the Middle East, to patrolling the North Atlantic and vital NATO sea lanes.

This variety of missions, and embracing of robust air power and naval forward presence helped drive the US to embrace the super carrier in the 50's, after temporarily successful efforts by the Air Force in the late 40's to kill earlier designs. While the British were faced with a shrinking empire, up and down economy, and loss of great power status, their navy including carriers slowly transitioned from a broad spectrum force to by the end of the Cold War on focused heavily on leveraging their position to focus on anti submarine warfare on the Greenland-Iceland-UK line. Though the importance of carriers as forward airfields was ably stated in the Falklands when Argentinian aircraft had only a few minutes of fuel to attack while the Brits could maintain a present CAP with their Harriers(though they had short legs too), the Argentines carrier was kept in safe water for fear of attack by RN subs after they bagged the General Belgrano cruiser. Many older US Essex class carriers experienced the same transition, as their usage in operating heavier modern jets waned their usage as anti sub carriers extended their lives by decades sometimes. While the newer super carriers could serve as the attack platforms and the centerpiece of offensive patrols or ground strikes. In a hot Cold War all in the name of ensuring that reinforcements could cross the Atlantic unmolested and fight it out on the plains of Germany.

The USSR though was in a very different place, they were for the most part already where they expected to fight and didn't need to take a plane or boat to get there. Thus they didn't have long sea lanes to protect or lack of airfields to support expected hot zones, though like all airfields they were stationary and fixed unlike a carrier. And their naval strategy was markedly different. They had 2 main goals, 1 was to protect undersea "Bastions" essentially heavily defended safezones where their ballistic missile subs could head to and be safe if the order came to launch. The other being to strike at NATO Sea Lanes. This was then achieved by using numerous fast attack subs, of nuclear and diesel varieties, surface ships firing big heavy and fast anti ship cruise missiles, and crucially long ranged shore based naval bombers and patrol aircraft. By the late Cold War a theoretical attack on a US Carrier Group might involve several soviet attack subs say Victor class nuke boat or a conventional Kilo, maybe a surface group of a Kirov battlecruiser a Kresta cruiser, and a gaggle of destroyers, and most importantly several dozen long ranged bombers. This would be split between the fast jet Backfires and the big ubiquitous turboprop Bears, all with the goal of saturating and overwhelming a battlegroups ability to meat all threats thanks to huge for their job missiles like the P-270, Kh-22, P-500 and P-700.

So what role for a carrier then? We see it in the limited USSR carrier projects, that aside from the ridiculous Stalin era plans that carriers were meant to simply augment this existing dynamic. To provide additional cover for the Bastions, and to protect surface task forces during the run in to missile launch. We can see this in the few classes of carriers the Soviets actually got completed, ignoring the Moskva's which are really just glorified DDH's and truly dedicated ASW platforms. That leaves us with the Kiev's and Kuznetsov's, both of which have very similar roles and the Kuznetsov's are really just enlarged improved variations on the same theme capable of operating non VSTOL aircraft from the get go. They were meant to simply defend their immediate vicinity to boil it down, and were even equipped with their own anti ship cruise missiles just like the surface combatants(if the trip is likely to be one way why not augment the striking power! this also had the benefit of allowing them to do the legal gymnastics of not calling them carriers and avoiding issues with them passing through the straits into the Black Sea). The Russians did flirt with larger designs over the years but it is a big step, and even the follow on to the Kuznetsov the Ulyanovsk would still have been a ski jump design and carry a large battery of anti surface missiles, though it was scrapped with the end of the Cold War only partly begun.

China faces many of the same issues, their primary concern is first ensuring the ability to defend their territory, then to meet enemies in the South China Sea and 11 Dash line of the first island chain. While for much of its existence the ability of the PLAN to project power any further towards the second chain of islands like Guam into the Pacific was simply not possible from a numbers or capability standpoint. Thus a reliance on Anti-Access/Area Denial strategy to protect the mainland and again usage of lots of shore based aviation since the foe mostly had to come to them and they were already mostly in range of what they wanted to hit to start a war (SK, Japan, the Philippines, Taiwan, etc.). This has changed though as China has sought to assert itself as a rising power.

So fast forward a few years the post Soviet slump meant no new ships and the Russians were left with what they had, hence the 1 Kuznetsov that was ready, and 4 Kiev's all of which were quickly withdrawn from service (2 sold as museums to China, 1 scrapped, and 1 heavily reconstructed and sold to India and in operation today). While the Kuznetsov has lunged from breakdown to breakdown never getting the care she really needs, her unfinished sister was taken by The Ukraine and eventually sold to China who finished her as the current Liaoning, and a near sister was just launched this week.

And in the end we should not dismiss the importance of prestige when it comes to having a carrier. Its just something "Great Powers" have and do. If Brazil can operate a carrier so can Russia. If France can make a nuclear carrier work why can't China? If Britain is building a modern 2 carrier fleet why shouldn't the world's largest democracy in India do so?

That said the future of carriers has often been a hot debate. No more so at any other time than today with rising costs, advancing A2/AD assets, and evolving faces of warfare. Even in the US questions about what shape the force should take remain in the open and sometimes contentious.

For a better understanding of the shape of the debate I would suggest checking out professional sites and sources, one of which is the US Naval Institute, their magazine is pay for view, but their blog regularly publishes excellent work on relevant topics. For instance this was a selected essay by a Midshipman from Annapolis on the PLAN's carrier outlook nd ambitions, perfect as an introduction: https://blog.usni.org/2015/07/20/capstone-essay-blue-waters-for-a-red-state-aircraft-carrier-operations-and-the-peoples-liberation-army-navy