With the end of the Cold War and the collapse of the Soviet Union, communism has largely been eliminated from consideration of viable or major economic systems. The two main surviving economic systems in the world today, then, are both variations of capitalism. One would be free market capitalism as practiced in the United States and much of Europea and Asia, and the other is more recent hybrid economic system combining the attributes of capitalism with a more substantial governmental role in the economy as developed first in Chile and later in China. This latter form of capitalism can be labeled "state-controlled" capitalism.
During much of the 20th Century, Socialism was a viable economic model, but continuing political changes in countries like West Germany, Britain and France -- in which conservative, free-market-oriented leaders alternated as the result of elections with more socialist-oriented politicians -- resulted in frequent dramatic shifts regarding levels of government ownership of major industries and movements to privatize those industries when conservatives were in power.
The China-model of economic system involves the use of capitalist principles in so far as companies are free to seek out markets and to compete among each other, but are still subject to considerable government control and, frequently, are actually owned by the government. The scale of China's economic growth over the past 30 years as lent considerable credibility and prestige to this model of economics. Recent financial difficulties, however, along with China's trade partners' growing discontent with Chinese government-imposed rules restricting foreign business activities have diminished that model to some degree.
The U.S. model of economic freedom, on the other hand, also saw its influence and prestige badly damaged by the financial crisis of 2008, in which massive government involvement in the private sector was needed to prevent large-scale bankruptcies in the automotive and banking sectors.
Despite those difficulties, the free market capitalist model and the government-sponsored enterprise model of China are the two major and dominant economic systems today.