Over the years, the names and precise duties of the Russian secret police have changed many times. This is a quick, and much simplified, list.
Cheka (ЧК), 1917‑1922 (Всероссийская чрезвычайная комиссия, 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 (НКВД), 1934-1946 (Народный комиссариат внутренних дел, 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 (КГБ), 1953 (or 1954)-1991 (Комитет государственной безопасности, Committee for State Security), all security agencies were folded into this one umbrella organization
FSB (ФСБ), 1991- (Федеральная служба безопасности Российской Федерации, Federal Security Service of the Russian Federation); 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"