Bell’s theorem states that no local stories can explain all quantum correlations we can observe. Indeed, the statistics of some quantum experiments using only local measurements violate some of the Bell inequalities, ensuring that this experiment cannot be described by any other theory that would be local. While it is known that all pure quantum states can lead to nonlocal correlations, it is still unclear which mixed states can produce some. This talk discusses two aspects of this question: 1. In the scenario initially considered by Bell we show how to construct an algorithm which for any state will decide if it can or cannot lead to nonlocality. 2. We present different possible extensions of the Bell scenario and give some recent results on one of them.