Characterizing Entanglement and Quantum Correlations Constrained by Symmetry This thesis focuses on the study and characterization of entanglement and nonlocal correlations constrained under symmetries. It includes original results as well as detailed methods and explanations for a number of different threads of research: positive partial transpose (PPT) entanglement in the symmetric states; a novel experimentally friendly method to detect nonlocal correlations in many body systems; the non equivalence between entanglement and nonlocality; and elemental monogamies of correlations. Entanglement and nonlocal correlations constitute two fundamental resources for quantum information processing as they allow novel tasks that are otherwise impossible in a classical scenario. However their elusive characterization is still a central problem in quantum information theory. The main reason why such a fundamental issue remains a formidable challenge lies in the exponential growth in complexity of the Hilbert space as well as the space of multipartite correlations. Physical systems of interest on the other hand display symmetries that can be exploited to reduce this complexity opening the possibility that some of these questions become tractable for such systems. Introduction Background PPT Entangled Symmetric States Nonlocality in Multipartite Quantum States Relating Entanglement and Nonlocality Atomic Monogamies of Correlations Conclusions and Outlook.