The recent contamination of quantum information science, statistical mechanics, and condensed matter has revealed unexpected and potentially very fruitful connections between these areas of research. We review some of the most important results on the properties of entanglement in quantum cooperative systems, concentrating on interacting spin systems and fermionic and bosonic models at zero temperature. We discuss the behavior of entanglement at and away from quantum criticality and the different roles played by bipartite and multipartite nonlocal correlations. Schemes for the generation and manipulation of entangled states by means of many-body Hamiltonians are reviewed as well. Furthermore, we report on very recent investigations of factorization points, factorized ground states, and "entanglement phase transitions" in quantum many-body systems. We show how newly developed methods allow to determine rigorously existence, location, and exact form of separable ground states in a large variety of, generally non-exactly solvable, quantum spin models belonging to different universality classes. We conclude with a tentative assessment on the prospects of understanding quantum complexity in the light of quantum entanglement theory.