Abstract: Over the last several years, three crucial shortcomings of the Cold Dark Matter (CDM) model have been discovered on galaxy-size scales. I present new observations addressing two of these problems: the missing satellite problem and the central density problem. I describe results from a Keck spectroscopic survey of the ultra-faint dwarf galaxies orbiting the Milky Way that were recently discovered by the Sloan Digital Sky Survey. We measure the masses of these galaxies based on their stellar kinematics and investigate whether they can account for the missing CDM satellites. I also present a rotation curve analysis of eight nearby low mass disk galaxies, based on high-resolution 2D velocity fields in Halpha and CO. This observing program has been designed to overcome some of the limitations of other rotation curve studies that rely mostly on long-slit spectra or low-resolution HI observations. We find that these objects exhibit the full range of dark matter density profiles between constant density and NFW halos, in contrast to the single universal density profile seen in CDM simulations. We consider possible explanations for the differences between observed and expected density profiles and argue that they are consistent with being caused by halo triaxiality.