Entanglement is one of the key features of quantum mechanics. We will see that nonlocal games provide a mathematical framework for studying entanglement and the advantage that it can offer. We will then take a closer look at graph-isomorphism games where two provers aim to convince a verifier that two graphs are isomorphic. It turns out that this operational definition leads to a notion of quantum isomorphisms which, surprisingly, admits a natural reformulation in the languages of quantum groups and counting complexity.