  Even if Dark Matter (DM) is neutral under electromagnetism, it can still
interact with the Standard Model (SM) via photon exchange from
higher-dimensional operators. Here we classify the general effective operators
coupling DM to photons, distinguishing between Dirac/Majorana fermion and
complex/real scalar DM. We provide model-independent constraints on these
operators from direct and indirect detection. We also constrain various
DM-lepton operators, which induce DM-photon interactions via RG running or
which typically arise in sensible UV-completions. This provides a simple way to
quickly assess constraints on any DM model that interacts mainly via photon
exchange or couples to SM leptons.
