Beginning in 1939, the factory's passenger cars were sold under the Moskvitch (Muscovite, a person whose origin or place of residence is Moscow) brand.

The plant was originally under the authority of Gorkovsky Avtomobilny Zavod (GAZ – Gorky Automobile Factory) founded at about the same time, but by 1939 it was operationally independent.

AZLK's role in the Soviet automotive industry was the production of small cars, which could be classified as anywhere from compact to mid-size.

AvtoVAZ and IZh were also charged with producing vehicles in the same category as AZLK, while GAZ handled the large car and full-size segment.

The construction of the plant called Moscow Car Assembly Factory (Russian: Московский автосборочный завод) began in 1929.

In May 1945, the Council of People's Commissars of the USSR adopted a decision on the production of small cars named "Moskvich".

In 1956, MZMA launched into production its own and highly successful model, the Moskvitch-402, that was followed by the upgraded and restyled versions known as the M-403 and M-407 and later by the brand new Moskvitch-408 series.

[1]: 164  The 355 was further developed into the 356 between 1973 and 1975, with "much bolder front end styling", new suspension, and an enlarged 1,799 cc (109.8 cu in) version of the DM engine with twin Zenith carburetors, giving 103 hp (77 kW; 104 PS), with a Borg-Warner transmission planned.

[1]: 168 In order to replace the 408 and M-412,[1]: 168  in 1975 Moskvitch designed a four-door fastback C1 (Series One), with a 1,702 cc (103.9 cu in) version of the DM straight four, offering 81 hp (60 kW; 82 PS), to give a top speed of 93 mph (150 km/h).

[1]: 167  It did not reach the company's goals and was never built, but inspired the four door C2 in 1976, which never passed the mockup stage, and the C3, which was very similar but a five-door hatchback.

As of 2022, the brand restarted production in the Russian market with the use of licensed Chinese vehicles making use of a factory that was once owned by Renault.