This thesis reports on experiments with quantum degenerate atomic mixtures and molecular gases at ultracold temperatures. The work describes the first realization of a quantum degenerate Fermi-Fermi mixture of two different species with unequal masses. In addition, the first quantum degenerate three-species mixture is realized. Furthermore, the first heteronuclear bosonic molecules with temperatures close to quantum degeneracy are created from a two-species mixture. The heteronuclear Fermi mixture adds the mass ratio and the different internal structure as new parameters to quantum degenerate...