This review aims to give an overview of the contribution of the Hubble Space Telescope to our understanding of the detailed properties of Local Group dwarf galaxies and their older stellar populations. The exquisite stable high spatial resolution combined with photometric accuracy of images from the Hubble Space Telescope have allowed us to probe further back into the history of star formation of a large variety of different galaxy types with widely differing star formation properties. It has allowed us to extend our studies out to the edges of the Local Group and beyond with greater accuracy than ever before. We have learned several important things about dwarf galaxy evolution from these studies. Firstly we have found that no two galaxies have identical star formation histories; some galaxies may superficially look the same today, but they have invariably followed different paths to this point. Now that we have managed to probe deep into the star formation history of dwarf irregular galaxies in the Local Group it is obvious that there are a number of similarities with the global properties of dwarf elliptical/spheroidal type galaxies, which were previously thought to be quite distinct. The elliptical/spheroidals tend to have one or more discrete episodes of star formation through-out their history and dwarf irregulars are characterized by quasi-continuous star-formation.