Lubyanka Prison was originally the headquarters of The All Russia Insurance Company, designed by Alexander V. Ivanov in 1897. After the Bolshevik Revolution, the government seized the building and converted it to the headquarters of the Cheka (secret police). In Soviet Russian jokes, it was referred to as the tallest building in Moscow, since Siberia (a euphemism for the Gulag labor camp system) could be seen from its basement.

It was used by the Checka, the NKVD, and the KGB. After the dissolution of the KGB, the Lubyanka became the headquarters of the Border Guard Service of Russia, and houses the Lubyanka prison and one directorate of the Federal Security Service of the Russian Federation (FSB). In addition, a museum of the KGB was opened to the public.

The Lefortovo Prison, sits in The Southeastern, Moscow District, was named after a close associate of Tsar Peter the Great, Franz Lefort. It was built in 1881 and used by the Tsar's secret police before the Bolshevik Revolution, followed by the Checka, the NKVD, the KGB, and the FSB.

The Kremlin actually had a prison in it's substructure during the 16th century, under the Tsars, including Ivan the Terrible.

The Butyrka Prison was originally built in the 17th century by Catherine the Great, but was reconstructed in 1879. One of it's most famous inmates was the founder of the KGB, Felix Dzerzhinsky . It is currently the largest prison in Moscow, and used primarily for remand prisoners.

More Info: en.wikipedia.org