The Gaia mission has provided distance and velocity measurements of over a billion stars in the Milky Way, making it the largest stellar catalog at hand. Simultaneously, recent developments in cosmological simulations have made it possible to track stars and dark matter in realistic Milky Way-like galaxies. In this talk, I will demonstrate how using cutting-edge simulations and Gaia data in tandem has enabled us to draw the first local map of the cold dark matter phase space distribution in our Galaxy. We find that the velocity distribution of dark matter is out of equilibrium, since it includes new velocity substructures that originated from previously-undetected galaxy mergers. This has extensive ramifications both for our understanding of the formation of the Milky Way, and for direct dark matter searches.