Abstract: Recent years have seen a growth of interest in the possibility of dark matter that interacts electromagnetically. While charged dark matter is largely ruled out, recent papers have explored the possibility of dark matter with either a magnetic or electric dipole moment. Here I will discuss another possibility: dark matter with an anapole moment. This is the only allowed electromagnetic moment for Majorana fermions, and it produces a model with several interesting differences from magnetic or electric dipole dark matter. In particular, a dark matter particle with a mass on the order of 10 – 100 GeV is ruled out for dipole dark matter, but it is allowed for anapole dark matter, and it lies just below the current XENON100 limits. I will also briefly discuss several spin-off results from this project, related to cosmological limits on dark matter properties.