Various topics at the interface between condensed-matter physics and the physics of ultra-cold fermionic atoms in optical lattices are discussed. This article starts with basic considerations on energy scales, and on the regimes in which a description by an effective Hubbard model is valid. Qualitative ideas about the Mott transition are then presented, both for bosons and fermions, as well as mean-field theories of this phenomenon. Antiferromagnetism of the fermionic Hubbard model at half-filling is briefly reviewed. The possibility that interaction effects facilitate adiabatic cooling is discussed, and the importance of using entropy as a thermometer is emphasized. Geometrical frustration of the lattice, by suppressing spin long-range order, helps revealing genuine Mott physics and exploring unconventional quantum magnetism. The importance of measurement techniques to probe quasi-particle excitations in cold fermionic systems is emphasized, and a recent proposal based on stimulated Raman scattering briefly reviewed. The unconventional nature of these excitations in cuprate superconductors is emphasized.