The combinatorial growth of the Hilbert space makes the many-electron problem a grand challenge. Progress relies on the development of non-perturbative methods, based on either wavefunctions or self energies. This made, in recent years, calculations for strongly-correlated materials a reality. These simulations draw their power from three sources: theoretical advances, algorithmic developments and the raw power of massively parallel supercomputers. Turning to quantum hardware could give quantum materials science the ultimate boost. Before quantum parallelism can be exploited, however, many questions, algorithmic and engineering, need to be addressed. The school will provide students with an overview of the state-of-the-art of many-body simulations and the promises of quantum computers. After introducing the basic modeling techniques and the concept of entanglement in correlated states, lectures will turn to methods that do not rely on wavefunctions, comparing density functional theory, the GW method and dynamical mean-field theory. Advanced lectures will broaden the discussion, addressing topics from the Luttinger-Ward functional to non-equilibrium Green functions. As a glimpse of future possibilities, the basics of quantum computing and its possible uses in materials simulations will be explained. The goal of the school is to introduce advanced graduate students and up to the full range of modern approaches for the realistic simulations of strongly correlated materials with computers.