The observation of neutrinoless double beta decay would have far-reaching consequences for particle physics. Most prominently, it would give a hint on the origin of neutrino masses and on the scale, at which they are generated. In this talk I will focus on the effective description of non-standard scenarios triggering neutrinoless double beta decay and on implications of their hypothetical observation. Particular attention will be paid to the short-range mechanisms, which, given current experimental limits, correspond to new physics at scales of a few TeV. The microscopic description of neutrinoless double beta decay including a thorough calculation of relevant nuclear matrix elements and phase-space factors allows for the estimation of the corresponding effective couplings and it can also help to pinpoint the dominant mechanism. Moreover, as the low-energy neutrinoless-double-beta-decay-contributing operators can be encoded in terms of the Standard Model effective operators violating lepton number by two units, it is possible to study the interplay between lepton number violation at high and low energy scales. Specifically, the contribution of the SM effective operators to the rate of neutrinoless double beta decay can be correlated with the washout of lepton number induced by the same operators in the early universe, and thus potentially constrain mechanisms of high-scale baryogenesis.