A socialist republic is a republic that according to its constitution or political doctrine operates under some form of a socialist economic system.
Many socialist republics operate under their own interpretation of Marxism, and sometimes claim to be implementing the dictatorship of the proletariat. In some socialist republics, an institutionalized party based on communist ideology is often in power. Therefore these republics are called communist states in the West.
Some nations go so far as to actually use the words socialist republic in their official name, for example the Democratic Socialist Republic of Sri Lanka or the "Socialist Republic of Vietnam". The Soviet Union and Yugoslavia consisted of socialist republics, and the country's full names were the Union of Soviet Socialist Republics and Socialist Federal Republic of Yugoslavia, respectively.
Other nations that have claimed to be socialist republics include North Korea, the People's Republic of China, and Cuba.
Since there are several different definitions of "socialism", a country's claim to the label of "socialist republic" is almost always disputed. Indeed, there are many socialists who strongly oppose certain self-proclaimed socialist republics.