Air supremacy
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.
The Soviets were so shaken by the staggering losses sustained by their allies that they dispatched the deputy head of their air defense force to Syria to examine how the Israelis had been so dominant.
The Israelis have upheld substantial air superiority for most of this time with Israel able to operate almost unopposed; Israel held near air supremacy against targets anywhere within range in the Middle East and North Africa until today. Regarding aircraft procurement, Israel started with British and French designs, then transitioning to indigenous production and then also design before moving again to purchasing to American designs. The Arabs directly participating in these battles against Israel except for Jordan and, to some extent, Iraq have commonly used Soviet designs.

Falklands War: In the Falklands War (2 April–20 June 1982), the British deployed Harrier jets as air superiority fighters against Argentina's Mach-capable  Dassault Mirage IIIEA fighters and subsonic Douglas A-4 Skyhawk jets. Despite the Sea Harrier's numerical and performance disadvantages, the British Harrier force suffered no air-to-air losses for over twenty Argentine aircraft shot down in aerial combat. Argentine airpower targeted Royal Navy ships during the landings at San Carlos Bay, numerous British vessels were lost or moderately damaged. However, many British ships escaped being sunk due to the Argentine pilots releasing their bombs at very low altitude, and hence those bomb fuzes did not have sufficient time to arm before impact and thus many never exploded. The pilots would have been aware of this—but released at such low altitudes due to the high concentration of British SAMs, Anti-Aircraft Artillery (AAA), and Sea Harriers, many failed to climb to the necessary release point. The Argentine forces solved the problem by fitting improvised retarding devices, allowing the pilots to effectively employ low-level bombing attacks on 8 June.

Gulf War: The Iraqi Air Force suffered almost complete obliteration in the opening stages of the Persian Gulf War (2 August 1990 – 28 February 1991). It lost most of its aircraft, as well as command-and-control capability, to precise Coalition strikes or when Iraqi personnel flew their aircraft to Iran. Iraqi Anti-aircraft defenses, including shoulder-launched surface-to-air missiles, were surprisingly ineffective against coalition aircraft, suffering only 75 aircraft losses in over 100,000 sorties, of which 42 of these were the result of Iraqi action while the other 33 were reportedly lost to accidents. In particular, RAF and US Navy aircraft which flew at low altitudes to avoid radar were particularly vulnerable, though this changed when the aircrews were ordered to fly above the AAA.

Post Cold War: During the 1980s, the United States commenced work on a new fighter capable of gaining air superiority without being detected by an opposing force, approving the Advanced Tactical Fighter program to develop a replacement for the United States Air Force's (USAF) aging F-15 fleet. The YF-23 and the YF-22 were chosen as the finalists in the competition. During 2005, the F-22 Raptor, the subsequent result of the program, became operational. USAF officials have promoted the F-22 as being a critical component of the service's tactical air power. Its combination of stealth, aerodynamic performance, and avionics systems is said to enable unprecedented air combat capabilities.
Anthony Cordesman wrote of NATO's theater air supremacy during its 1999 intervention in the Kosovo War of 1998–1999. According to several reports, including reports by the Carnegie Endowment for International Peace and Bulletin of the Atomic Scientists that quote Russian sources, the Russian Federation has in recent decades formulated explicit strategies for using tactical nuclear weapons. These new strategies have in part resulted from the assumption of obtaining air supremacy and use by the U.S. Air Force of precision munitions with little collateral damage in the Kosovo conflict in what amounted to quick mass destruction of military assets once only possible with nuclear weapons or massive bombing against fellow Slavic Serbians; it also assumed that Russia and its allies do not have the strategic economic capacity of current NATO and allied nations to meet this threat with conventional weapons. In response Vladimir Putin, then secretary of the Security Council of Russia, developed a concept of using both tactical and strategic nuclear threats and strikes to de-escalate or cause an enemy to disengage from a conventional conflict threatening what Russia considered a strategic interest. This concept was formalized when Putin took power in Russia in the following year.
Throughout the Syrian Civil War of the 2010s, Israel was reportedly able to hold a general stance of air superiority over the Syrian forces, enabling offensive operations with relative impunity. However, this was challenged during 2018 by the deployment of a Russian-supplied S-400 missile battery to the Syrian theatre. During the February 2018 Israel–Syria incident, despite the loss of an aircraft, Israel has demonstrated their capability to operate without effective interference within the Syrian theater. On 22 May 2018, Israeli Air Force chief Amikam Norkin said that the service had employed their F-35Is in two attacks on two battle fronts, marking the first combat operation of an F-35 by any country.

See also: Air superiority fighter
Battleplan (documentary TV series)
Canadian Forces aerospace doctrine
Command of the sea
Defense Technical Information Center
No-fly zone
Overmatch
Suppression of Enemy Air Defenses
Technological supremacy
Victory Through Air Power and its film

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External links: Air Power In Peripheral Conflict: The cases of Korea and Vietnam
Defense Technical Information Center
Australian Department of Defence
Col. John A. Warden III. The Air Campaign: Planning for Combat. June 2000.
Encyclopædia Britannica
Glossary of Nato Definitions Archived 22 January 2000 at the Wayback Machine
The Luftwaffe and the battle for air superiority: Blueprint or warning
RAND Study of U.S. Fighter Design