The Lambda Cold Dark Matter (LCDM) framework successfully accounts for observational constraints on large (> 1 Mpc) scales, from the clustering of galaxies to the angular dependence of the Cosmic Microwave Background to the structure and matter content of galaxy clusters. On the scale of individual galaxies and, in particular, of dwarf systems much fainter than the Milky Way, a number of apparent conflicts with LCDM expectations have been reported. These have prompted the consideration of a number of radical modifications to LCDM, such as the possibility that dark matter might be "self-interacting", or that it might not be “cold”. I will review the status of these alleged problems and will report on recent work that reevaluates the observational evidence and reexamines the role of systematic uncertainties in the comparison between observation and model predictions. In particular, I will propose a possible resolution to the “cusp vs core” problem that requires no cores; an explanation for the mass discrepancy-acceleration relation that requires no changes to the mass profile of LCDM halos; and a plausible origin for the enigmatic population of galaxies inhabiting “extremely cold” dark matter halos, such as the recently discovered Crater 2 satellite.