  Ultracold atomic gases provide a fantastic platform to implement quantum
simulators and investigate a variety of models initially introduced in
condensed matter physics or other areas. One of the most promising applications
of quantum simulation is the study of strongly-correlated Fermi gases, for
which exact theoretical results are not always possible with state-of-the-art
approaches. Here, we review recent progress of the quantum simulation of the
emblematic Fermi-Hubbard model with ultracold atoms. After introducing the
Fermi-Hubbard model in the context of condensed matter, its implementation in
ultracold atom systems, and its phase diagram, we review landmark experimental
achievements, from the early observation of the onset of quantum degeneracy and
superfluidity to demonstration of the Mott insulator regime and the emergence
of long-range anti-ferromagnetic order. We conclude by discussing future
challenges, including the possible observation of high-Tc superconductivity,
transport properties, and the interplay of strong correlations and disorder or
topology.
