The nature of cold dark matter is one of the big unsolved questions in physics. A wide spectrum of astronomical observations from small galaxies to the largest scales can be consistently explained by the presence of dark matter, in an amount equal on average to about five times the mass in ordinary matter. It is empirically known that no known particle can be cold dark matter, and many theories exist for dark matter as a new elementary particle. Numerous searches for particle dark matter are under way, with controversial claims of discovery: production at high-energy accelerators, detection in underground observatories, indirect evidence through cosmic rays, gamma rays, and peculiar stars. In my talk, I will present some challenges in constructing theories of particle dark matter, remarking the tension between simplicity and experimental constraints, the contrast between first-principle and empirical formulations, and the difficulty of some unsolved problems at the frontier of the field.
