The Matra MS80 was designed by Gérard Ducarouge and Bernard Boyer and built in the brand's workshops in Vélizy-Villacoublay, on the outskirts of Paris.

It was one of the first F1 cars designed to use wings to produce downforce.

The chassis was an aluminum monocoque, reinforced with an anterior multitubular structure. The suspensions used double wishbones on the front while at the rear an upper link, a lower quadrilateral and longitudinal arms were used that rested on the rear bulkhead of the chassis, behind the cockpit. The concentric spring/damper assemblies were mounted outside the bodywork. The fuel tanks had structural functions, installed on the chassis sidepods, on each side of the driver.

At that time, the brands ran their own teams and managed to profit from the projects by selling chassis to private teams. In 1969 Matra Sports did not participate with its works team and delivered its two chassis to Ken Tyrrell team, who had made his debut in Formula 1 the previous year.

At his team's headquarters in Surrey, UK, Tyrrell equipped the MS80s with the new Cosworth DFV engines. The engine was connected to the bulkhead at the rear end of the chassis and the engine / gearbox assembly had structural functions, following the innovation of the Lotus 49. The gearbox was from Hewland and the tires from Dunlop.

The service drivers were Jackie Stewart and Jean-Pierre Beltoise. The team took full advantage of the loss of competitiveness at Lotus, which had to revise the model 49 after the failure of the 63, and won 6 victories, all with Jackie Stewart.

At the wheel of the MS80, Jackie Stewart became the only driver with a private team to achieve a World Champion title, and Team Tyrrell was the only private team to become World Champion of Constructors.

The relationship between Ken Tyrrell's team and Matra was very fruitful, but of short duration. Indeed, for the following year, the French brand imposed the use of its V12 engines.

Ken Tyrrell's refusal motivated the split, with his team using the new chassis of the newly created March in 1970, before Derek Gardner designed the team's first own car.

Matra would not be very successful in its remaining F1 adventure, having abandoned the top category at the end of 1972.

It would return in 1976 as an engine supplier for Ligier, and would definitely abandon F1 at the end of the 1982 season.