Probing Dark Matter Throughout Cosmic History

I will review the status of cosmological searches for dark matter-baryon interactions, summarizing the best current limits on scattering of sub-GeV particle candidates with protons derived from the CMB anisotropy measurements. I will then present stringent new bounds on the same physics, inferred recently from the observed population of the Milky Way satellite galaxies. I will highlight complementarities between different observations and discuss the prospects for the coming decade, especially in context of the next-generation CMB observations.