  This PhD tutorial article is a review of our experiments on heteronuclear
quantum gas mixtures at the University of Hamburg. We introduce basic
properties of trapped Fermi-Bose mixtures and demonstrate the achievement of
large quantum degenerate mixtures of 40K and 87Rb. Using heteronuclear Feshbach
resonances, we show how the heteronuclear interaction can be tuned, allowing us
to induce phase separation and collapse for large repulsive and attractive
interactions, respectively. We realize Fermi-Bose mixtures in 3D optical
lattices as a novel quantum many-body system and study coherence properties of
the mixture. Combining our experiments on lattices and Feshbach resonances, we
present the first realization of ultracold heteronuclear Feshbach molecules.
The molecules are created at individual sites of a 3D optical lattice. We
discuss lifetime, binding energy and rf association efficiency in terms of a
universal model and give an outlook for possible future developments.
