"Communism refers to a theoretical system of social organization and a political movement based on common ownership of the means of production."

This was never achieved in history. In so-called Communist states a political elite (not "the people" or anything else that could be called common owners) had direct rulership over the means of production, therefore it is more correct to call these states "Socialist".

http://en.wikipedia.org/wiki/Communism
http://en.wikipedia.org/wiki/Socialism