Dwarf galaxies in the Local Group cornerstones for stellar astrophysics and cosmology

Dwarf galaxies have been the crossroad of significant theoretical and observational efforts, but we still lack firm constraints concerning their formation and evolution. They are also fundamental laboratories to investigate the impact of the environment on star formation and on chemical evolution in stellar systems that are order of magnitudes smaller than giant galaxies. We present some recent results concerning the dwarf spheroidal Carina and the dwarf irregular IC10. In particular, we focus our attention on the evolutionary properties of their stellar populations using accurate and deep color-magnitude diagrams. We also briefly discuss the impact that the transition from old, low-mass (horizontal branch) to intermediate-age (red clump) helium burning stars has in constraining the star formation history of complex stellar systems.