Abstract
In 1964, Bell showed that an entirely classical experimenter can certify that two spatially-separated parties share quantum entanglement by playing a game with them. In this talk, I will survey a recent line of research that combines Bell's work with classical techniques from the study of interactive proof systems, to design games that certify not just the presence of entanglement but specific, many-qubit states and operators. I will give an outline of the main techniques used as well as applications to delegated quantum computation and to quantum complexity theory, including a quantum analog of the classical PCP theorem.