What are the main political-economic theories of the 20th century that are currently in effect?
I assume that you asking which political-economic theories that were present in the 20th century are still present today. If so, the main economic theory still in effect today is capitalism. The main political theory is democracy though there are still countries in which totalitarianism (which may or may not be seen as political theory) is still in effect.
Most countries of the world today are more or less capitalist in their economics. The ideas of socialism and communism have more or less been abandoned by all major countries of the world.
Most countries are also moving toward democracy. There are some major exceptions to this rule as countries like China (in particular) and Russia (to some extent) are still run by totalitarian governments.