The mass range and specific properties allowed for these particles strongly depend on models and other constraints (e.g. the cosmological abundance), and, except for axion-like-particles, the relevant energy range for detection with astrophysical photons roughly goes from 10 keV (sterile neutrinos as warm/cold DM) to 1 TeV (supersymmetric candidates). Some candidates may annihilate or decay into photon lines (gamma+neutrino is typical for decays), which provides a clear signature. The MeV energy range is particularly interesting for those DM candidates that have been invoked to contribute the intense 511 keV line emission arising from the Galactic Center, whose full origin remains undetermined. Since the dominant part of this emission must come from positronium decay, electrons and positrons originating in DM annihilation or decay must be injected with MeV energies at most, constraining the DM mass range or the mass splitting in case of excited DM models (no strong mass constraint in the latter case). Annihilation into charged lepton pairs is prototypal for MeV astronomy since it is necessarily accompanied by final state radiation corrections, which induce hard photon spectra, and therefore potentially observable signals whose intensity should somehow trace the DM distribution in targets.