John Clifford "Cliff" Garrett founded the company in Los Angeles in 1936. Garrett AiResearch was a manufacturer of turboprop engines and turbochargers, and a pioneer in numerous aerospace technologies. It was previously known as Aircraft Tool and Supply Company, Garrett Supply Company, AiResearch Manufacturing Company, or simply AiResearch. In 1964, Garrett AiResearch merged with Signal Oil & Gas to form a company renamed in 1968 to Signal Companies, which in 1985 merged with Allied Corp. into AlliedSignal. In 1999 AlliedSignal acquired Honeywell and adopted the Honeywell name.

The Company's first major product was an oil cooler for military aircraft. Garrett designed and produced oil coolers for the Douglas DB-7.[3] Boeing's B-17 bombers, credited with substantially tipping the air war in America's and Great Britain's favor over Europe and the Pacific, were outfitted with Garrett intercoolers, as was the B-25. The Company developed and produced the cabin pressure system for the B-29 bomber, the first production bomber pressurized for high altitude flying. By the end of World War II, AiResearch engineers had developed air expansion cooling turbines for America's first jet aircraft, the Lockheed P-80 Shooting Star.

In the late 1940s and early 1950s, Garrett was heavily committed to the design of small gas turbine engines from 20 - 90 horse power (15 - 67 kW).

During the 1950s AiResearch initiated activities in the field of aircraft electronics, and designed and produced a wide range of military and industrial products for aerospace and general industry. It focused on fluid controls and hydraulics, avionics, turbochargers, aircraft engines, and environmental control systems for aircraft and spacecraft. By 1960 Garrett gas turbines, cabin pressurization systems, air conditioners, and flight control systems were aboard the Convair 880, Lockheed Super Constellation, Vickers Viscount, Sud Aviation Caravelle, Douglas DC-8, and Boeing 707. The company had also developed the first inflatable airliner evacuation slides.

In the 1950s and 1960s Garrett pioneered the development of foil bearings, which were first installed as original equipment on the McDonnell-Douglas DC-10 in 1969 and then became standard equipment on all U.S. military aircraft. In the 1960s, AiResearch Environmental Control Systems provided the life supporting atmosphere for American astronauts in the projects Mercury, Gemini, Apollo, and Skylab.

By 1962, Garrett was powering the world’s first turbocharged production car, the Oldsmobile Jetfire Rocket. This was followed by several other firsts, including the first turbocharged car to win the Indianapolis 500 (1968), the first turbo for a non sports car application (1977-Saab 99), the first mass production turbo for diesel engines (1978-Mercedes 300SD), and the first turbo to win the 24 Hours of Le Mans (1978-Renault).