Nonlocal quantum correlations are not only intriguing, but also serve as an indispensable resource for device-independent (DI) quantum information processing. Within the DI paradigm, conclusions are drawn directly from the raw data measured without relying on any additional assumption about the preparation nor the measurement devices. Prominent examples of this are the possibility to generate shared secret keys, or random numbers that are provably secure assuming only general physical principles. Here, we are particularly interested in using the observed nonlocal correlations to characterize the underlying state and/or the measurement devices.