The problem of strongly interacting Fermi gases has been with us for a long time. When the interaction is attractive and weak, one can resort to the BCS solution. When the interaction is strong enough, bound states form and one has effectively a system of composite bosons, that undergo BEC at low enough temperatures. What happens in the intermediate region? How is the BCS state related to BEC? The answers to these questions represent one of the most interesting many-body problems, with applications that range from cold atoms to dilute neutron matter. While many qualitative statements follow from symmetry and scale invariance arguments, a reliable quantitative description has so far only been achieved with Monte Carlo simulations. In this talk I will explain how these simulations are done, explain their advantages and shortcomings and show results for the caloric curve, ground-state energy and critical temperature along the crossover, with particular emphasis on the so-called unitary point.