"Artificial crystals" made of ultra-cold atoms trapped by laser beams can be engineered with a remarkable level of controllability, and allow for the study of quantum physics in previously unexplored regimes, hence opening up new frontiers between condensed matter physics and quantum optics. I will review various aspects of this field, including the trapping, cooling and probing of fermionic atoms into the Mott and Néel states. I will also address recent theoretical and experimental studies of transport in such systems.