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 Fermi gases. The molecular cloud being close to quantum degeneracy marks the first starting point for the realization of a heteronuclear molecular BEC and to investigate the BEC-BCS crossover with unequal masses. Moreover, the molecules can be transferred into the rovibrational ground state to create a polar BEC with an anisotropic, long-range interaction.