  Dwarf galaxies may play a key role in the formation and evolution of bigger
systems. This make a topic of major interest knowing how they form and evolve
and, in particular, how their star formation histories (SFHs) have proceed
since their birth. For nearby galaxies, the color-magnitude diagram (CMD)
contains stars formed over all their lifetime. It is hence a fossil record of
their SFHs. The analysis with synthetic CMDs provides a powerful tool to
retrieve them.
  In this paper, I discuss the critical issues related to the computation of
synthetic CMDs, present a short summary of the currently available results for
the SFH extending the full life of galaxies and make a few critical
considerations about the powerfulness and back-draws of the method.
