Lada is the "export" brand name
of the "Zhigulye" brand, produced by "VAZ
" ("Volzhskiy Avtomobilniy Zavod" = "The Vogian Automotive Factory").
Even though less prestigious than the Volga's (GAZ) or Chaikas/ZIMs, those were one of the most well-regarded car brands in the Soviet Union, surpassing the reputation of Moskvitches (AZLKs) and Zaporozhetzes (ZAZs).
This comes mostly from superior design and quality, which in turn comes from the fact that the factory in Toliati they were built in was built by the FIAT, during the times of cooperation between Italy and USSR in the late 1960s.
The first model (the 2101, or the 1-Series) was produced starting from 1970 and was almost identical to the FIATs of that time. Actually - it still looks quite nice, though I wouldn't want to drive one.
It influenced heavily all of the Cold War era Ladas, most of which were small 5-passenger sedans with a gross weight of about 1 metric ton, and engine displacement between 1.3 and 1.6 litres - not much fun.
The exception could be the rugged VAZ-2121 "Niva" cross-country vehicle (but not a SUV), that was quite successful in (other) 3rd world countries.
Many Ladas are still on the road in ex-Soviet Union.
Currently VAZ produces some new Lada models that could possibly compete with Kias and Hyundais... but maybe not :-).
The official website is http://www.vaz.ru/.