In Marxist-Leninist states, the party is seen as "the vanguard of the people" and therefore usually has the power to control the state, and the non-state party officials in the politburo generally hold extreme power.
In the Soviet Union for example, the General Secretary of the Communist Party did not necessarily hold a state office like president or prime minister to effectively control the system of government. Instead, party members answerable to or controlled by the party held these posts, often as honorific posts as a reward for their long years of service to the party. On other occasions, having governed as General Secretary, the party leader might assume a state office in addition. For example, Mikhail Gorbachev initially did not hold the presidency of the Soviet Union, that office being given as an honour to former Soviet Foreign Minister Andrei Gromyko. Stalin ruled the Soviet Union for well over a decade before assuming the governmental position of Premier of the Soviet Union during World War II.
Officially, the Party Congress elects a Central Committee which, in turn, elects a General Secretary. Under Stalin however, this model was essentially reversed and it was the General Secretary who determined the composition of the Politburo and Central Committee.
In Trotskyist parties, the Politburo is a bureau of the Central Committee tasked with taking day-to-day political decisions, which must later be ratified by the Central Committee. It is appointed by the Central Committee from among its members. The post of General Secretary carries far less weight than in the Stalinist model. See, for example, the Lanka Sama Samaja Party.