The Sinatra Doctrine was a policy adopted by the Soviet Union in 1989. The term was used by the Soviet Foreign Ministry spokesman, Gennadi Gerasimov, in reference to the Frank Sinatra song "My Way." On that date, the USSR officially stated that they would allow Warsaw Pact nations to make their own decisions instead of being forced to follow (Russian) Communist beliefs and practices.
Countries included in the Warsaw Pact were the Soviet Union, of course, and Albania, Bulgaria, Czechoslovakia, East Germany, Hungary, Poland, and Romania. This pact allowed for Soviet military bases on these countries' territories, along with an overarching military command. It lasted from 1955 to 1991, although some countries withdrew earlier than the final end date. As the Sinatra Doctrine only came into effect in 1989, for the most part the countries involved were more or less under the thumb of the Soviet Union.
It was a significant step for the Soviet government to announce the Sinatra Doctrine. It represented a new way of looking at alliances and the treatment of other nations. By stating that each country has a right to manage its own affairs and make its own decisions, even if those choices were contrary to Soviet preferences, the Soviet Union showed that it was ready to work as a partner, not only a leader.