Over the years, the names and precise duties of the Soviet secret police have changed many times.  This is a quick, and much simplified, list.

Cheka, 1917‑1922 (All-Russian Extraordinary Commission for Combating Counter-Revolution and Sabotage), originally set up by Feliks Dzerzhinskii

GPU, 1922-1934 (State Political Administration); later technically renamed the OGPU, 1923-34 (Regional State Political Administration)

NKVD, 1934-1946 (Peoples Commissariat of Internal Affairs), key heads included Genrikh Yagoda, Nikolai Ezhov and Lavrentii Beria; changed name to NKGB, 1943-1946 (Peoples Commissariat of State Security)

MGB, 1946-1953 (Ministry of State Security); functioned along with the MVD (Ministry of Internal Affairs); key leader was Lavrentii Beria

KGB, 1953 (or 1954)-1991 (Committee on State Security), all security agencies were folded into this one umbrella organization

FSB, 1991- (Federal Security Service); the KGB formally ended with the dissolution of the USSR in 1991 and was replaced by several agencies, the most relevant being the FSB, which currently functions with a number of different purposes. An article appeared in Foreign Affairs (September-October 2010) about the FSB: Andrei Soldatov and Irina Borogan, "Russia's New Nobility: The Rise of the Security Services in Putin’s Kremlin"