Understanding the star-forming histories of dwarf galaxies is of vital importance if we are to make the connection to cosmological issues such as the nature of faint blue galaxies or the shape of the halo mass function. Making such a connection requires that we understand the statistical properties of dwarf galaxies in general. Examples of peculiar star-forming histories in galaxies such as NGC 205 are a clear warning that we do not really know what regulates star formation in dE galaxies, but are of no use for larger issues until we know how prevalent such phenomena are. Do cluster dE's share the same episodic star formation seen in local dwarfs (Sect. 4.1)? Do they follow the same scaling of metallicity with luminosity, surface brightness, and velocity dispersion?
In models where star formation in dE's is governed purely by internal processes (e.g. feedback from supernovae or OB stars), the stellar populations of dE galaxies should be purely determined by their structural parameters, and not by their environment. However, there are a number of observations that suggest that environment is important in governing both the numbers and the morphology of dwarf ellipticals. Examples are: (1) evidence of multiple episodes of star formation in local dE's, reviewed below; (2) confinement of most Milky Way companion dE's to the plane of the Magellanic stream (Sect. 6.2); (3) systematic variations in the dwarf/giant ratio from rich clusters to loose groups (4) significant differences in the spatial distribution of nucleated and non-nucleated dE's in the Virgo and Fornax clusters, the nucleated dE's being more centrally concentrated (see Sect. 6); and (5) large scatter in the trends of color and absorption-line strengths (Brodie and Huchra 1991) with luminosity among cluster dE's (see Sect. 4.2).