In this talk I will try to give an introduction to the mathematical framework of quantum computing, completely disconnected of the underlying theory of quantum physics. After an exposition of a circuit model for quantum computing, we will split those circuits into two parts (the infamous Alice and Bob) and talk about the behaviours of those bipartite systems, more specifically somewhat counter-intuitive phenomenons like entanglement and nonlocality. Finally, we will see how those phenomenons are relevant in the study of communication complexity, and discuss recent results.