Recently, there have been hints for dark matter (DM) annihilation in the Galactic center to one or more photon lines. In order to achieve the observed photon line flux, DM must have a relatively large effective coupling to photons, typically generated radiatively from large couplings to charged particles. When kinematically accessible, direct annihilation of DM to these charged particles is far too large to accommodate both the DM relic density and constraints from the observed flux of continuum photons from the Galactic center, halo and dwarf galaxies. We discuss three exceptions to these obstacles, generating the observed line signal while providing the correct relic density and evading photon continuum constraints. The exceptions are (i) coannihilation, where the DM density is set by interactions with a heavier state that is not populated today, (ii) forbidden channels, where DM annihilates to heavier states that are kinematically blocked today, but open in the early Universe, and (iii) asymmetric DM, where the relic density is set by a primordial asymmetry. We build simple models to realize these scenarios.