Ultracold atoms provide a unique avenue for designing and studying many-bodyquantum systems. In particular, the Fermi-Hubbard model, which is animportant element of modern condensed matter theory, can be experimentallyexplored with fermionic atoms in optical lattices. A very appealing featureis the capability to change smoothly from non-interacting to attractive orrepulsive interactions by accessing a Feshbach scattering resonance.

I will report on experiments with interacting fermionic atoms inthree-dimensional optical lattices. We have been able to directly image theFermi surface of the atoms in the optical lattice and to observe thetransition of the system from a conducting state to a band insulator. Usinga Feshbach resonance we access the strongly interacting regime, formingmolecules in the optical lattice and dynamically inducing a coupling betweenthe lowest energy bands. Recent results concerning the behaviour of thesystem for attractive interactions will be presented.