The theoretical description of many-body systems, be it molecular or extended, from first principles has been one of the principal goals of the physical sciences since the advent of quantum mechanics. This is unfortunately an exceptionally complicated endeavour, especially so in the so called strongly correlated'' systems. These are characterized by their qualitative behavior being dominated by particle-particle interactions, which precludes their accurate description using effective one-body approaches, such as Kohn-Sham density-functional theory. As a consequence of their remarkable complexity, strongly correlated materials present a wide palette of exciting collective phenomena of huge technological interest. Paradigmatic examples are high temperature superconductors based on transition metal oxides or pnictides, materials presenting colossal magnetoresistance, or iron/molybdenum based catalytic centers in biological systems. With the ample range of potential applications in mind, from energy conversion and storage to the development of new principles for information processing devices, great interdisciplinary effort, combining condensed matter physics, quantum chemistry and materials science, has been dedicated over the last decades to devising and applying accurate theoretical and numerical approaches for the description and prediction of electronic properties arising from strong correlation.