The fighter was born on April 1st, 1915.  Roland Garros, a French pilot, got his first victory in the air with his Moraine Saulnier aircraft equipped with a forward firing machine gun, the first in history.  Other planes had guns in the front, like the Vickers Gunbus, but they had gunners.  The true effectiveness of the fighter wasn't achieved until a fixed gun was controlled by the pilot. He achieved this feat by attaching metal wedges on his propeller to deflect any bullets that might hit it.  Within two weeks he was an ace.  The solution he used was pretty hard on propellers, shattering some of them anyway. He was forced down later that month, and once Anthony Fokker saw his plane he quickly developed the interrupter gear that made the fighter into the ultimate killing machine of the air.

pic of Morane Saulnier

The United States have developed the ultimate fighters of modern times, the F-22 and the F-35, which can not only carry huge payloads, but get them there without being discovered by radar.  However, even their reign will come to an end soon.  Cheap computers and sensors will soon make their life miserable in the air, and their role will be to get some payloads in the air, to be released and hunt on their own, leaving the fighters to vacate the area as quickly as possible before they are hunted and killed by swarms of networked hunter/killer missiles.

The US has been in this game for a while now, starting as long ago as 1998 with their LOCAAS or Low Cost Autonomous Attack System.  This reduces the size of the warhead and makes it better to adapt to conditions on it's own, without any influence from the pilot of the aircraft carrying it.  This system has already morphed into the SDB or the Small Diameter Bomb System.  The system extends the standoff range, guides itself with GPS and INS (Inertial Navigation System), and also carries anti-jam and anti-spoofing modules.  The size is smaller to reduce collateral damage, but it is still a killer, able to penetrate three feet of reinforced concrete.  And if they are destroyed in the air, we lose no humans or expensive F-35's.  

picture of SBS

Another thing that will kill fighters will be the inability and cost to protect aircraft carriers.  Other countries are developing weapons that will swarm the target, each equipped with different sensors and networked together, making a carrier quite a tempting target.  It will be much cheaper to outfit a lot of Arleigh Burke class destroyers delivering the same ordnance, with smaller cross sections  to attack.  The US has developed the Long Range Anti-Ship Missile (LRASM) mostly because the Chinese already have better anti-ship missiles than we do.  It has been successfully tested and has autonomously flew long range, identified and hit the target.  On it's own.  

diagram of LRASM's use

Other countries may not be able to match the US's sophistication in these matters, but they are plenty capable of building autonomous systems on their own, and sometimes cheaper is better, as you can build lots more of them, potentially swamping the defense of a ship at sea.  The aircraft carrier may not disappear, but like the battleship before it, it's time is almost up.

References

Birth of the fighter plane, 1915

Rise of the Missile Carriers, US Navy Institute

The Diplomat -LRASM