We report on the investigation of correlations between quantum degenerate atoms. The realization of a strongly interacting fermi gas in a 3D optical lattice has opened the way to experimentally simulate problems from condensed matter physics. Using a Feshbach resonance, we control the scattering between different atomic spin states and induce tunable interactions between the atoms. Depending on the sign of the interaction we populate higher Bloch bands or convert pairs of atoms into molecules. Deeply bound molecules are localized at the lattice sites and from the fraction of formed molecules we measure the temperature of the atoms in the lattice. A different powerful experimental tool to study correlations in ultracold atomic vapors is single atom counting by cavity QED techniques. Using this method, the first and the second order correlation funtion of quantum gases becomes directly measurable.