Air supremacy
Korean War: The Korean War represented a major turning point for aerial warfare, being the first conflict in which jet aircraft played the central role in combat. Once-formidable fighters such as the P-51 Mustang, F4U Corsair, and Hawker Sea Fury—all piston-engined, propeller-driven, and designed during the Second World War—relinquished their air superiority roles to a new generation of faster, jet-powered fighters arriving in the theater. In the initial months of fighting, the P-80 Shooting Star, F9F Panther, Gloster Meteor and other jets under the UN flag dominated the Korean People's Air Force (KPAF) propeller-driven Soviet Yakovlev Yak-9 and Lavochkin La-9s. By early August 1950, the KPAF was reduced to only about 20 planes.
However, with the Chinese intervention in late October 1950, the KPAF begun receiving the MiG-15, which was one of the world's most advanced jet fighters at that time. Equipped with not only jet propulsion but also a swept wing, the MiG-15 quickly outclassed the straight-wing United Nations fighters. In response, the United States dispatched three squadrons of its own swept-wing fighter, the F-86 Sabre, which arrived in the theatre in December 1950. The Sabre reportedly claimed kill ratios as high as 10 to 1 against the MiGs, allegedly shooting down 792 MiG-15s and 108 other aircraft in exchange for 78 Sabres that were lost to enemy fire. Meanwhile, the Grumman F9F Panther, a straight-wing carrier-based jet, became the mainstay of the USN during the period and had a relatively good showing, possessing a 7:2 kill ratio against the more powerful MiG-15.

Vietnam War: During the Vietnam war the US side, especially over the north, had restrictive rules of engagement often requiring visual identification nullifying the advantage they would have had using beyond visual range missiles though possibly avoiding friendly fire due to IFF systems not being ubiquitous on US strike aircraft.  In the 1950s, the United States Navy tasked the F-8 Crusader, known affectionately as the "Last Gun Fighter" as their close-in air superiority fighter. This role would be taken over by the F-4 Phantom, which was designed as a missile armed interceptor. The USAF had developed the F-100 and F-104 as air superiority fighters, though by the Vietnam war had already phased out the F-100 from all but air support missions and the fast but slow turning F-104 allegedly deterred attacks and despite losses scored no victories in air combat but in the USAF was also replaced by the F-4 by 1967.  Especially under the rules of engagement imposed on them the 'Century Series" aircraft initially specifically designed for intercepting heavy nuclear bombers or delivering tactical nuclear weapons were found to be wanting when they were engaged by the very agile fighters Mikoyan-Gurevich MiG-17 and Shenyang J-6 provided to the VPAF by the USSR and PRC; the Mikoyan-Gurevich MiG-21 while less agile was formidable against the F-4 and traded range for very high performance.  This imbalance lead to the USAF ordering variants of the F-4 with an internal 20mm gun, and both the USAF and USN sometimes flying with centerline gun pods on aircraft not equipped with an internal gun.
In the 1960s, the limited agility of American fighters in dogfights over Vietnam led to a revival of dedicated air superiority fighters, which led the development of the "Teen Series" F-14, F-15, F-16 and F/A-18. All of them made close-combat manoeuvrability a top priority, and were equipped with guns absent from early Phantoms. The heavy F-14 and F-15 were assigned the primary air superiority mission, because of their longer range radars and capability to carry more missiles of longer range than lightweight fighters.

Arab–Israeli wars: From 1948, when Israel reestablished independence from a protective League of Nations mandatory regime managed by the UK, the neighbouring countries have, to varying degrees, disputed the legitimacy of a Jewish state in a majority Arab region.  Some neighbouring states have in the last few decades recognized and signed peace treaties; all have ceased large scale conventional warfare to overrun Israel in large part due to an increasing ability to impose Israeli air supremacy over the region's airspace when required.

1948 war: The Israeli Air Force formed in 1948 with the formation of the modern State of Israel. Israel was involved in the 1948 Arab–Israeli War immediately after the end of the British mandate in Palestine. The air force initially consisted of mainly donated civil aircraft, a variety of obsolete and surplus ex-World War II combat-aircraft were quickly sourced by various means to supplement this fleet. Creativity and resourcefulness were the early foundations of Israeli military success in the air, rather than technology which, at the inception of the IAF, was generally inferior to that used by Israel's adversaries. In light of the complete Arab theater air supremacy, and the bombing and shelling of existing airbases, the first Israeli military-grade fighters operated from a hastily constructed makeshift airbase around the current Herzliya Airport, with fighters dispersed between the trees of an orange orchard. As the war progressed, more and more Czechoslovak, American, and British surplus WWII-era aircraft were procured, leading to a shift in the balance of power.

1956 war: In 1956, Israel, France, and the United Kingdom occupied the Sinai Peninsula after Egypt closed the Straits of Tiran to Israeli ships, sparking the Suez Crisis. Israel's new French-made Dassault Mystere IV jet fighters provided air cover for the paratroop transport aircraft. The Egyptian tactic was to use their new Soviet-made MiG-15 jets as fighter escorts, while their older jets conducted strikes against Israeli troops and vehicles. In air combat, Israeli aircraft shot down between seven and nine Egyptian jets with the loss of one plane, but Egyptian strikes against the ground forces continued through to 1 November. After several sorties were launched by French and British aircraft, President Gamal Abdel Nasser ordered his pilots to withdraw to bases in Southern Egypt. The Israeli Air Force was then free to strike Egyptian ground forces at will.

1967 war: In 1967, the Straits of Tiran were again closed and international peacekeepers were ejected by Egypt. Israel then initiated Operation Focus. Israel sent nearly every capable combat aircraft out against the vastly larger Egyptian Air Force, holding only four for protection. Egyptian airfields were destroyed with anti-runway penetration bombs and the aircraft were mostly destroyed on the ground; Syria and Jordan also had their air forces destroyed when they entered the conflict. This is one of the preeminent examples of a smaller force seizing air supremacy where Israel had complete control of the skies above the entire conflict area.

War of Attrition: Following the Six-Day War, from 1967 to 1970, there were small scale incursions into the Israeli-held Sinai desert as Egypt rearmed. This evolved into large-scale artillery and air incursions in 1969, with Soviet pilots and SAM crews arriving to assist in January 1970. The strategy was to engage Israeli aircraft in surprise fighter encounters near the Suez Canal where Egyptian SAMs could be used to assist fighters. Syrian, North Korean, and Cuban pilots assisting also suffered losses in this period. In August 1970, a cease-fire was agreed on.

1973 war: The first few days of the 1973 Yom Kippur War saw major Arab ground breakthroughs, surprising Israel who, after its lopsided 1967 victory, considered its air supremacy sufficient to blunt or dissuade any conventional attack. Despite Egypt and Syria having rebuilt their air forces since 1967, Israel continued to deny them the airspace over the battle area; however, these Arab forces were able to control losses and shoot down Israeli air support aircraft by employing mobile surface to air weaponry which travelled along with invading units. Most of Israel's air power in the first few days was directed to reinforce the badly mismatched garrison overlooking the besieged Golan Heights which was under attack by Syria. After weakening the Arab SAM cover with airstrikes, commando raids, and armored cavalry, the Arab armored units outran their mobile SAM cover and Israeli aircraft began to take greater control of Egyptian skies, permitting Israeli landings and establishing a beachhead on the west bank of the Suez canal. When Egyptian fighter aircraft were sent into the area of the Israeli bridgehead, SAM sites were offlined which allowed Israeli air power to more safely engage and destroy many Egyptian fighters though taking some losses.

1978 Lebanon conflict: The 1978 South Lebanon conflict was an invasion of Lebanon up to the Litani River, carried out by the Israel Defense Forces in 1978 in response to the Coastal Road massacre. Israel had complete air supremacy.

1982 Lebanon invasion: In the 1982 Lebanon War where Israel invaded up to Beirut, Syria intervened on the side of Lebanon and the PLO forces residing there. Israeli jets shot down between 82 and 86 Syrian aircraft in aerial combat, without losses. A single Israeli A-4 Skyhawk and two helicopters were shot down by anti-aircraft fire and SAM missiles. This was the largest aerial combat battle of the jet age with over 150 fighters from both sides engaged. Syrian claims of aerial victories were met with skepticism even from their Soviet allies.