We present detailed star formation and chemical enrichment histories obtained for six isolated Local Group galaxies in the context of the LCID (Local Cosmology from Isolated Dwarfs) project. One of the main goals of the LCID project was to investigate the influence of global processes (like cosmic reionization) or internal mechanisms (such as SNe feedback) on the evolution of dwarf galaxies. We show that all the galaxies in the sample, including those that ended star formation very early on, formed most of their stars after reionization was complete. This demonstrates that reionization alone was not able to stop star formation in these galaxies, as had been expected.