The talk will focus on quantum no-signalling correlations and their subsets of quantum commuting, approximately quantum, quantum and local correlations, exhibiting a chain of correlation classes, similar to the analogous chain for classical no-signalling correlations. I will describe some canonical objects associated with quantum no-signalling correlations, such as the universal operator system and the universal C*-algebra of a stochastic operator matrix, and will formulate characterisations of the correlation classes in terms of states on various operator system tensor products. Finally, I will describe a quantum version of non-local games and discuss how quantum no-signalling correlations can be used as strategies for those games. The talk will be based on a joint work with Lyudmila Turowska.