I visited Vietnam over the summer and I believe they are still under Communism. I dont know much about it though.
its the philosophical, social, political and economic ideology and movement whose ultimate goal is the establishment of the communist society, 
Are there a lot of countries under communism?
The goal is the establishment of socioeconomic order structured upon the common ownership of the means of production and the absence of social classes, money and the state.
I see. When was this ideology first conceived?
ideologies grouped around both. All of these share the analysis that the current order of society stems from its economic system, capitalism; that in this system there are two major social classes; that conflict between these two classes is the root of all problems in society; and that this situation will ultimately be resolved through a social revolution.
The two classes are the working class—who must work to survive and who make up the majority within society—and the capitalist class—a minority who derives profit from employing the
Communism
In political and social sciences, communism (from Latin "", "common, universal") is the philosophical, social, political, and economic ideology and movement whose ultimate goal is the establishment of the communist society, which is a socioeconomic order structured upon the common ownership of the means of production and the absence of social classes, money, and the state.
Communism includes a variety of schools of thought, which broadly include Marxism and anarchism (anarcho-communism), as well as the political