Could Dark Matter be Electromagnetic?

One of the leading candidates for dark matter is a weakly-interacting massive particle (WIMP), with an annihilation cross section typical of the weak interaction.  However, recent years have seen a growth of interest in the possibility that dark matter interacts electromagnetically.  While charged dark matter is largely ruled out, recent papers have explored the possibility of dark matter with a magnetic dipole moment, an electric dipole moment, or an anapole moment.  I will review the standard "freeze-out" calculation for thermal dark matter and show why charged dark matter is ruled out, while higher order multipoles are not.  Direct detection experiments sharply constrain electric or magnetic dipole dark matter, but are less restrictive for anapole dark matter.  On the other hand, LHC data already require the anapole dark matter mass to be greater than 100GeV.  Several spin-off ideas will also be discussed.