MIP* (pronounced “M-I-P star”) denotes the class of problems that admit interactive proofs with quantum entangled provers. It has been an outstanding question to characterize the complexity of MIP*. Most notably, there was no known computable upper bound on MIP*. We show that MIP* is equal to the class RE, the set of recursively enumerable languages. In particular, this shows that MIP* contains uncomputable problems. Through a series of known connections, this also yields a negative answer to Connes’ Embedding Problem from operator algebras. In this talk, I will explain the connection between Connes' Embedding Problem, quantum information theory, and computational complexity. I will then give an overview of our approach, which involves reducing the Halting Problem to the problem of approximating the entangled value of nonlocal games. Joint work with Zhengfeng Ji, Anand Natarajan, Thomas Vidick, and John Wright.