For nearly 40 years, dark matter has been widely assumed to be cold and collisionless. Cold dark matter models make fundamental predictions for the behavior of dark matter on small (<10 kpc) scales. These predictions include cuspy density profiles at the centers of dark matter halos and a halo mass function that increases as dN/dM ~ M^-1.9 down to very small masses. We suggest two observational programs relying on extremely large telescopes to critically test these predictions, and thus shed new light on the nature of dark matter. (1) Combining adaptive optics-enabled imaging with deep spectroscopy to measure the three-dimensional motions of stars within a sample of Local Group dwarf galaxies that are the cleanest dark matter laboratories known in the nearby universe. From these observations the inner slope of the dark matter density profile can be determined with an accuracy of 0.20 dex, enabling a central cusp to be distinguished from a core at 5 sigma significance. (2) Diffraction-limited AO imaging and integral field spectroscopy of gravitationally lensed galaxies and quasars to quantify the abundance of dark substructures in the halos of the lens galaxies and along the line of sight. Observations of 50 lensed arcs and 50 multiply-imaged quasars will be sufficient to measure the halo mass function over the range 10^7 < M < 10^10 Msun at cosmological scales, independent of the baryonic and stellar composition of those structures. These two observational probes provide complementary information about the small scale structure, with a joint self-consistent analysis mitigating limitations of either probe. This program will produce the strongest existing constraints on the properties of dark matter on small scales, allowing conclusive tests of alternative warm, fuzzy, and self-interacting dark matter models.
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