Despite the key role dark matter has in the composition and evolution of the universe, its identity remains unknown, and dark matter candidates abound. I have devised stronger constraints on key dark matter properties by how they imprint themselves onto astrophysical structures. I show that a classical challenge to the widely accepted cold dark matter paradigm, the missing satellites problem, the conundrum that there are fewer satellites observed around the Milky Way than found in simulations, is solved down to 10^8 Msun. This implies that that warm dark matter models with a thermal relic mass smaller than 4 keV are in tension with satellite counts, putting pressure on the sterile neutrino interpretation of recent X-ray observations. I also show that dark matter self-interactions, which were believed to produce large separations between the galaxy and dark matter distributions in merging galaxy clusters, do not, implying that galaxy-dark matter offsets are unlikely to generate competitive constraints. However, after the dark matter halos coalesce, the galaxies oscillate around the center of the merger remnant on stable orbits with amplitudes that scale strongly with the self-interaction cross section. Observed BCG offsets may constrain the self-interaction cross section to 0.1 cm^2/g---one of the tightest constraints yet.