Abstract: The study of quantum correlations goes back to the 1960s, when John Bell first observed that local measurements on an entangled system can give rise to a nonlocal correlation (J. Bell Physics, 1964). Studies of quantum correlations have led to excited demonstrations of the quantum advantage. My research focuses on the applications of quantum correlations in device-independent cryptography, and the characterizations of quantum correlations. I will first introduce device-independent randomness generation and randomness expansion protocols, which have been realized in experiments. Then, I will discuss how quantum correlations allow us to certify an unknown quantum device with pure classical interactions. Lastly, the conceptual question about quantum correlations is whether we can get a finite-length description of the set of quantum correlations of the same size. I will try to answer it from the computational complexity perspective.