Abstract: Neutrinoless double-beta decay is the most powerful tool to probe not only for Majorana neutrino masses but for lepton number violating physics in general. We discuss relations between lepton number violation, double-beta decay and neutrino mass, review a general Lorentz-invariant parametrization of the double-beta decay rate, highlight a number of different new physics models showing how different mechanisms can trigger double-beta decay and, finally, discuss possibilities of discriminating and testing these models and mechanisms in complementary experiments.