Quantum theory is known to lead to correlations between the outcomes of measurements performed on distant systems that are strictly stronger than those obtained by any classical theory. Such correlations, termed nonlocal, highlight the radical departure of quantum theory from classical formulations of physics. Here, we study fundamental questions about the nature of nonlocal correlations in quantum theory, using as a tool the recently developed field of EPR steering. In the second part of the thesis, we construct new methods for the certification of the dimension of quantum systems and apply our techniques to quantum random number certification.