We will discuss quantum no-signaling correlations introduced by Duan and Winter with focus on its different subclasses (quantum commuting, quantum and local). They will appear as strategies of quantum-to-quantum non-local games. We will then discuss concurrent quantum non-local games, as quantum versions of synchronous/bisynchronous non-local games focusing on quantum graph homomorphism/isomorphism games, and provide tracial characterisations of their perfect strategies belonging to various correlation classes; e.g. the perfect strategies for quantum graph isomorphism game are given by tracial states on the universal C∗-algebra of the projective free unitary quantum group. This is a joint work with Michael Brannan, Sam Harris and Ivan Todorov.