Dwarf galaxies may play a key role in the formation and evolution of bigger systems. This makes it a topic of major interest to know how they form and evolve and, in particular, how their star formation histories (SFHs) have proceeded since their birth. For nearby galaxies, the colour-magnitude diagram (CMD) contains stars formed over their full lifetime. It is hence a fossil record of their SFHs. Analysis via synthetic CMDs provides a powerful tool to retrieve them. In this paper, I briefly present the critical issues related to synthetic CMD analysis and make a summary of the currently available results for the SFH extending over the full lifetimes of galaxies.