China is in theory a socialist government, working towards a communist ideal. Thing to note is that no country has every achieved true communism in the political theory sense, though the Soviet Union, China, Cuba and others supposedly have that as a goal.
In practice, China is a cross between a oligarchy (small elite group) and gerontocracy (elders) with a repressive streak. They certainly do crack down on dissidents, though things have been opening up. Right now China faces a huge problem as they really have no idea where many millions of people who've migrated from the countryside to cities live.
What's interesting is that we have diplomatic and business relations with China, which has a formidable nuclear arsenal, yet we don't with Cuba. Hmm, same supposed types of government....

