Dwarf galaxies are a frontier for new discoveries in both galaxy formation and cosmology. I discuss work centered around connecting LCDM and its predictions to observations of dwarf galaxies at three different scales of "dwarf". I will discuss the Milky Way's satellites and both solutions and lingering troubles with their abundances and scalings. The strangest of these puzzles manifest in the bright dSphs, which seem to be under-dense relative to LCDM expectations. With this in mind, I present results from a large spectroscopic survey of M31's dSph satellites searching for signs of similar puzzles. These reveal consistency between the Milky Way and M31 satellite populations, showing these puzzles are not unique to the Milky Way. Finally, I will describe a search for bright satellites (analogous to the LMC) in the SDSS, and compare their abundances and properties to straightforward LCDM expectations. These reveal an amazing level of consistency between the SDSS and LCDM for bright satellites. Taken together, these results suggest that there is a particular scale in galaxy formation (at Vcirc~50 km/s), where either LCDM begins to break down or galaxy formation becomes overwhelmingly stochastic.