In this talk, I will introduce an operator-algebraic formulation of robust self-testing in terms of states on C*-algebras. For synchronous games and similar nonlocal games, self-testing can be studied through tracial states on the associated game algebras. For these nonlocal games, I will show how the stability of the tracial states determines the robustness of a self-test. I will also discuss self-testing in the commuting operator framework. Based on arXiv:2301.11291 (with Connor Paddock, William Slofstra, and Yangchen Zhou), arXiv:2411.03259, and arXiv:2505.05994 (with Matthijs Vernooij).