Today, there is no longer any coherent ideology that challenges liberal democracy for world supremacy in an overt way. There is no longer a communist bloc that is attempting to broaden its influence across the world. However, there is at least one ideology that appears to be an alternative (if not a challenge) to liberal democracy. What I am talking about could be called something like statism or command capitalism.
What I am calling statism or command capitalism is a system in which the economy is not so closely controlled as it is in communism. At the same time, however, the economy is not as free as in a liberal economy. The major example of such an economy today is China. China's economy has major aspects of capitalism, but is still directed to a great extent by the state.
In states like China, the government keeps fairly close control of people's lives (like by censoring the internet) but does not really have any other ideology other than trying to keep power. This means it is not a communist form of government, regardless of the name of its ruling party.
Because China is rising, you can argue that its political economy is being offerred as an alternative to liberal democracy and capitalism.