Short answers, pulled from the story.
On the 18th of April 1915, a French aviator named Roland Garros was shot down behind enemy lines, and his aircraft along with its secret synchronization gear was captured by the Germans. This event triggered a competitive cycle of improvement that defined aerial warfare for the next century.
The first victory using synchronization gear came on the 1st of July 1915 when Leutnant Kurt Wintgens of the German Feldflieger Abteilung 6 downed a Morane-Saulnier Type L. This victory ushered in the Fokker Eindecker which gave German forces a period of air superiority known as the Fokker scourge.
The German Messerschmitt Bf 109 and the Soviet Polikarpov I-16 faced off during the Spanish Civil War which provided the necessary testing ground for new technologies. The Bf 109 proved superior and the lessons learned from these dogfights led to greatly improved models in World War II.
In 1944 the Messerschmitt Me 262 became the first operational jet fighter to enter combat primarily serving with the Luftwaffe's JG 7. It was considerably faster than contemporary piston-driven aircraft and proved quite difficult for Allied pilots to defeat in the hands of a competent pilot.
Most modern combat aircraft are fitted with a cannon typically between 20 and 30 millimeters in caliber. This follows the Vietnam War which proved that air-to-air missiles were often unusable at high speeds and that guns still had a role to play.
The fourth generation of fighters was significantly influenced by the energy-maneuverability theory developed by Colonel John Boyd and mathematician Thomas Christie. This approach emphasized aircraft designs capable of performing fast transients and quick changes in speed altitude and direction.