While hundreds of fighter pilots became aces (someone who has shot down at least five aircraft) during World War II, aces have been increasingly rare ever since. There were some during the thirty years after World War II ended in 1945. Mostly during the few wars that did get fought. The last pilot, of any air force, to qualify as an ace was Jalal Zandi of the Iranian Air Force, who shot down 14 Iraqi aircraft in the late 1980s, while flying a U.S. made F-14. While this trend has gone unnoticed by most, air forces have been studying this phenomenon intently.
There has been a lot less air-to-air combat since World War II. The main reason is nuclear weapons. While nearly 2,100 nuclear weapons have been detonated in the last 66 years, only two of these nukes were used in war. That was enough to terrify major nations into avoiding major (but not minor) wars. The continued existence of nuclear weapons created a new dynamic between the major military powers. This nuclear standoff came to be known as "mutually assured destruction" (MAD) during the Cold War. As a result of MAD, there has not been a war between the Great Powers in Europe since the surrender of Nazi Germany on May 8, 1945, a peace that has lasted 70 years so far. This is the longest period of major-power peace in Europe since before the fall of Rome 1500 years ago. The second-longest such period of peace among the European Great Powers was the 43 years between the end of the Franco-Prussian War (January 31, 1871) and the Austro-Hungarian declaration of war on Serbia (July 28, 1914), which signaled the outbreak of the First World War two days later. In effect, since November 5, 1988, every day that the European Great Powers have not been at war with each other has set a new European regional --and pretty much a world-- record for the duration of a peace.
But air force leaders want to be ready for the return of air-to-air combat. One thing they are sure of is that the conditions will be different. They already know that by observing the American experience. The other reason for the lack of air combat is the dominant position (in the air) of American warplanes (air force, navy and marines). American fighters, and their pilots, remain the best in the world. That's not preordained, or an accident, it's the result of a lot of hard work, willingness to learn from mistakes, and a whole lot of money. Meanwhile, the U.S. Air Force (and naval air) realize that no one has successfully challenged them for control of the air in over half a century but that could change with the rise of Chinese territorial and military ambitions. Dominating the air has its downsides, like being unprepared for the next air war. So American air combat commanders (both Navy and Air Force) worry about future threats, and how well prepared U.S. pilots will be to deal with them.
While there have been few aces since the 1940s, there have been several thousand air-to-air encounters by jet fighters. There’s enough data on nearly 2,000 of these encounters to do some analysis. What this has shown is a very clear trend in which electronics and long range missiles are becoming more important while aircraft speed and maneuverability is much less of a factor. Thus the growing appeal to upgrade older aircraft (including F-5s, F-4s and MiG-21s) with modern electronics that make them capable to using long range air-to-air missile (like the radar guided American AMRAAM or the Israeli Derby). A look-and-shoot helmet also tends to be part of the upgrade as well as better defensive (missile detecting and defeating) systems. These upgrades are considered formidable air-to-air opponents, at least on paper. At the same time unmanned aircraft are becoming more reliable, effective and capable and another growing threat to future aces.
All this has to be considered in light of the fact that shooting down enemy aircraft is not the primary mission of an air force. Aircraft became a factor in military affairs over a century years ago when they demonstrated their superior ability to see what the enemy was up. Most of the use of air power at the beginning was about reconnaissance, and preventing the enemy from seeing what you were doing. Between the world wars, the idea of using air power as an offensive weapon developed. This proved to be more of a factor at sea than on land. Reconnaissance remained the most useful service air forces provided.
Smart bombs and much improved sensors (on manned and unmanned aircraft as well as satellite) have turned many modern fighters into very effective bomb trucks. Training for that can be done on the ground in a simulator. Same with modern air-to-air combat, which is largely dependent on who has superior sensors and long-range missiles. Fighters still carry cannon, but for decades these have only seen use against ground targets and even that is rare.
The lack of major air campaigns with real opposition has meant a lot of knew ideas and solutions remain theoretical. Until put to the test of combat you can’t really be sure. What you can be sure of is that there has not been a lot of air-to-air combat for half a century and the last time a fighter pilot became an ace was in the 1980s. The future remains disturbingly murky.