The lower bound for the mass of a galaxy is unknown, as are the typical luminosity of the smallest galaxies and their numbers. The answers depend on the extent to which star formation in the first population of small mass halos may be suppressed by radiative feedback loops. If early populations of dwarf galaxies did form in significant number before reionization, their fossils should be found today in the Local Group. This paper reviews our ongoing efforts to simulate and identify fossil dwarfs in the Local Group. It is widely believed that reionization stopped star formation in fossil dwarfs. However, here we dispute this idea and discuss a physical mechanism whereby recent episodes of star formation would be produced in some fossil dwarfs that, hence, may characterized by a bimodal star formation history. The same mechanism could turn dark halos that failed to form stars before reionization into gas-rich dark galaxies. We believe that current observational data supports the thesis that a fraction of the new ultra-faint dwarfs discovered in the Local Group are fossil dwarfs and we predict the existence of a population of ultra-faint dwarfs with lower surface brightness than currently observed.
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