Probing the nature of dark matter with the CMB

After decades of searches, the nature of dark matter (DM) remains an unsolved problem. This forces us to look at existing models from new angles, and to explore (or re-explore) DM candidates beyond the standard weakly-interacting massive particle. In this talk, I will focus on what one can learn from the cosmic microwave background (CMB) frequency spectrum and anisotropies. After reviewing CMB physics, I will first describe how the CMB can test DM-baryon scattering. I will outline a recently developed Boltzmann-Fokker-Planck formalism, which allows to account for finite DM self-interactions in addition to scattering with baryons. In the second part of the talk, I will discuss an old DM candidate brought back to the front page by LIGO: primordial black holes (PBHs). I will describe the simple accretion model underlying CMB bounds to PBHs, as well as some directions of possible improvements to this calculation.