The Lambda Cold Dark Matter (LCDM) paradigm makes specific predictions for the abundance, structure, substructure and clustering of dark matter halos, the sites of galaxy formation. These predictions can be directly tested, in the low-mass halo regime, by dark matter-dominated dwarf galaxies. A number of potential challenges to LCDM have been identified when confronting the expected properties of dwarfs with observation. I review our understanding of a few of these issues, including the “missing satellites” and the “too-big-to-fail” problems, and argue that neither poses an insurmountable challenge to LCDM. Solving these problems requires that most dwarf galaxies inhabit halos of similar mass, and that there is a relatively sharp minimum halo mass threshold to form luminous galaxies. These predictions are eminently falsifiable. In particular, LCDM predicts a large number of “dark” low-mass halos, some of which should have retained enough primordial gas to be detectable in deep 21 cm or Hα surveys. Detecting this predicted population of “mini-halos” would be a major discovery and a resounding success for LCDM on small scales.