Now, however, even the communist Chinese seem to be living the American dream. Here, we look at how communism works and how it has influenced society today.
The definition of communism
According to the Oxford Dictionary, communism is a theory or system of social organisation in which all property is owned by the community and each person contributes and receives according to their ability and needs.
How communism works
For many people, the most familiar form of communism is that established by the Bolsheviks after the Russian Revolution of 1917.
Other countries that have adhered to this form of communism include the rest of the Soviet Union, China, Cuba and Vietnam.
However, China has followed its own ideological path of Communist development since the so-called Sino-Soviet split of the 1960s.
The history of communism
Communist theory, or Marxism, was expounded by the German philosopher Karl Marx and his associate Friedrich Engels, who believed that the overthrow of capitalism would eventually - via a transitional phase - give rise to a fully communist society, in which classes and the state are no longer present.
Following World War Two, more countries in Central and Eastern Europe became part of the Communist Soviet Union, China became the People's Republic of China, led by the Communist Party of China's Mao Zedong, and a number of third world states either adopted or imposed a Communist government.
And by the early 1980s, it is thought that almost one third of the world's population lived in Communist states, meaning that communism was seen as a major threat to western democracies and capitalism.
This rivalry peaked during the Cold War, as the world's two remaining superpowers, the United States and the Soviet Union fought for top spot in the arms and space races.
However, the power of the state in Communist societies grew rather than withering away, and cracks began to show by the 1980s, which is when communism in eastern Europe started to collapse.
The different kinds of communism
There are lots of different communist theories, usually named after their main exponents. These include Trotskyism, Leninism and Maoism.
Trotskyism, which is based on the theory expounded by Russian intellectual Leon Trotsky, declared the need for an international, rather than domestic, workers' revolution and a dictatorship of the proletariat based on democratic principles.
And Leninism, named after the first leader of Communist President Vladimir Lenin, stated that a vanguard party to lead the proletarian revolution and to secure all political power after the revolution for the working class is a necessary part of the transition from capitalism to communism.
Maoism, meanwhile, is the type of communism associated with Chinese leader Mao Zedong, who believed that communist and capitalist nations could not live in harmony and broke ties with the Soviet Union for its "revisionist" policy of maintaining relations with capitalist countries in the 1960s.
The arguments for and against communism
Advocates of communism argue that it is the only way to create a level playing field and ensure that all members of society can enjoy the same standard of living.
However, for many economists, the expansion, rather than the reduction, of the state's role in the Soviet Union and the union's eventual downfall is sufficient proof that communism does not work.