Dwarf galaxies are the most diffused type of galaxies in the Universe and were probably even more numerous in the past, when they might have contributed to the population of blue systems overabundant in deep galaxy counts (e.g. [1, 2]) and more likely to the assembling of larger baryonic systems. In spite of having received less attention than spiral and elliptical galaxies, dwarf galaxies have probably more cosmological relevance. For instance, late-type dwarfs are the preferred targets for cosmologists interested in Big Bang Nucleosynthesis, because their low metal and helium contents allow the derivation of the primordial helium abundance from HII regions spectra with minimum extrapolation (e.g. [3, 4, 5]). Moreover, their low metallicity and high gas content make them apparently less evolved than spirals and ellipticals, thus more similar to what primeval galaxies may have been.
One of the main cosmological interests is related to the possibility that today's dwarfs are the survivors of the building blocks of massive galaxies. Cold Dark Matter (CDM) cosmology predicts that dwarf systems are the first ones to form after the Big Bang, since only dark matter halos of mass smaller than 108 M are able to condense from primordial density perturbations. In this framework, more massive systems are assembled by subsequent merging of these protogalactic fragments (the hierarchical formation scenario; e.g. [6, 7]), and dwarfs have a pivotal role in the evolution of massive galaxies.
Observations do show that galaxies merge in the local Universe and that big galaxies accrete their satellites. We know the cases of the Magellanic Stream and of other streams connected to the Sagittarius dwarf spheroidal (dSph) and other satellites falling on the Milky Way (e.g. [8, 9]). Andromeda is quite similar in this respect (e.g. [10, 11, 12]), with streams and clumps just as, or even more than, our own Galaxy. The question is whether big galaxies form only by successive mergers of smaller building blocks, as proposed by the hierarchical formation scenario, or satellite accretion is a frequent but not necessary and dominant event, consistent with a downsizing formation scenario. Downsizing  in principle does not concern the hierarchy or the epoch of galaxy formation, it simply reflects the observational evidence that the bulk of stars in more massive galaxies formed earlier and at a higher rate than those in less massive systems. If mechanisms are found allowing for these star formation properties in the bottom-up scenario (e.g. [14, 15, 16]), then downsizing is not incompatible either with CDM or with the hierarchical scenario. However, downsizing is often seen as the alternative to hierarchical formation, replacing in this role the monolithical scenario, where each galaxy forms from the collapse (dissipative or dissipationless) of its protogalactic gas cloud. In the monolithical scenario more massive galaxies form much earlier than less massive ones for simple gravitational arguments , with timescales for the collapse of the protogalactic cloud originally suggested to be of the order of 100 Myr, and now more often considered of the order of 1 Gyr.
One of the effective ways to check whether or not big galaxies are made only by successive accretions of satellites like the current ones is to observe the resolved stellar populations of massive and dwarf systems and compare their properties with each other. If chemical abundances, kinematics and star formation histories of the resolved stars of massive galaxies are all consistent with those of dwarf galaxies, then the former can be the result of successive merging of the latter; otherwise, either satellite accretion is not the only means to build up spirals and ellipticals or the actual building blocks are not alike today's dwarfs.
An updated review of the chemical, kinematical and star formation properties of nearby dwarfs can be found in . In this tutorial paper we describe how the star formation history of a galactic region can be derived from the colour-magnitude diagram of its resolved stars, and we summarize what people have learnt on the SFHs of dwarf galaxies from the application of the most popular approach based on the CMD. In Section 2 we introduce the method; in Section 3 we describe in detail procedures and uncertainties; and in Section 4 we report on the results of its application on the SFH of dwarf galaxies. A discussion on how these results may affect our understanding of galaxy evolution is presented in Section 5.