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XMM-Newton and Chandra have ushered in a new era for the study of dwarf galaxies in the Local Group. We provide an overview of the opportunities, challenges, and some early results. The large number of background sources relative to galaxy sources is a major theme. Despite this challenge, the identification of counterparts has been possible, providing hints that the same mechanisms producing X-ray sources in larger galaxies are active in dwarf galaxies. A supersoft X-ray source within 2″ of the supermassive black hole in M32 may be a remnant of the tidal disruption of a giant, although other explanations cannot be ruled out.