The SFH of galaxies can be studied with detail in nearby systems which are resolvable into individual stars. In such case, the color-magnitude (CM) diagram can be plotted. Perhaps, the most powerful method nowadays available for the study of the SFH of galaxies is to compare their observed CM diagrams with sets of synthetic CM diagrams computed assuming different SFH scenarios and in which an accurate, realistic simulation of observational effects has been performed. In the present paper, we first review the different methods of computing synthetic CM diagrams and compare them with the observed ones and the different problems and limitations of such an analysis. Then, we discuss the overall properties of dwarf galaxies and the differences and connections between the two main subgroups into which they are divided (dIr and dE). Finally, we show recent results for the SFH of several nearby dIr (NGC 6822, Pegasus, LGS3 and Antlia) and dE (NGC 185, Phoenix and Leo I). In all the galaxies, including the dIrs, we find an important old to intermediate-age stellar population and a likely decreasing SFH. The most dIr-like galaxies (NGC 6822 and Pegasus) and also Antlia show an important star formation burst lasting the last few hundred Myr. An important young and intermediate-age stellar population is also found in Phoenix and Leo I, but NGC 185 shows only a few traces of recent or intermediate star formation activity.