Ours is a dark Universe: its astrophysical systems are but a minor addition to dark matter, whose abundance six times outweighs all other particles in the Universe. The physical nature of dark matter is a pressing question, whose answer will likely lead to discovery of new fundamental physics. I will discuss how the coming decade of cosmological observations will open up a wide new window into the physics of dark matter interactions, complementing terrestrial lab searches. In particular, I will review the status of current searches with data from the Planck satellite and present forecasts for the next-generation observations of the cosmic microwave background radiation. I will then use a recent claim of a potential detection of a dark-matter signal from a low-frequency radio observation of the epoch of Cosmic Dawn, in order to demonstrate the necessity for comprehensive analyses in establishing a discovery. Finally, I will discuss the potential of near-field cosmology enabled by upcoming galaxy surveys for uncovering the fundamental nature of dark matter.