The complexity of quantum many-body systems originates from the interplay of strong interactions, quantum statistics, and the large number of quantum-mechanical degrees of freedom. Probing these systems on a microscopic level with single-site resolution offers important insights. Here we report site-resolved imaging of two-component fermionic Mott insulators, metals, and band insulators using ultracold atoms in a square lattice. For strong repulsive interactions we observe two-dimensional Mott insulators containing over 400 atoms. For intermediate interactions, we observe a coexistence of phases. From comparison to theory we find trap-averaged entropies per particle of $1.0,k_{mathrm{B}}$. In the band-insulator we find local entropies as low as $0.5,k_{mathrm{B}}$. Access to local observables will aid the understanding of fermionic many-body systems in regimes inaccessible by modern theoretical methods.
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