Dwarf elliptical galaxies clearly have much to offer for studies of cosmology. The uniformity of their structure and their ubiquity in the local universe make them promising test particles and distance indicators. Correlations among their structural properties and their stellar populations offer clues to galaxy formation that we have yet to fully understand.
For the future, on the observational side we suggest that more detailed quantitative studies of the structure and stellar populations of cluster dE's are vital if we are to provide serious constraints on models for their formation. Samples must be chosen to represent the full range of surface-brightness, morphology, and position in a cluster before we can have a clear idea which parameters are most important. Detailed studies of the stellar populations and luminosity function of the nuclei are also essential if we are to understand how they fit into the process of galaxy formation.
On the theoretical side, the most promising models for explaining the surface-brightness-metallicity-luminosity relations appear to be those with slow, self-regulated star formation, and metal-enhanced winds. Environmental effects such as sweeping or triggered star formation may act in addition, but probably do not dominate the evolution of most dE's. However, some sort of environmental influence seems essential to explain the clustering properties of dE's. The most promising ideas appear to be dE formation from tidal debris as a way of accounting for the high dwarf/giant ratio in clusters, and pressure-induced star formation as a way of accounting for the central concentration of nucleated dE's within clusters. However, much work remains to be done before such ideas can even be tested against the luminosity function, clustering properties, or frequency of nucleation of dE galaxies.
We would like to thank numerous colleagues for providing us with preprints, reprints, references, and especially ideas for this review. We are particularly grateful to Patricia Vader, Brian Chaboyer, Ortwin Gerhard, and Sidney van den Bergh for allowing us to reproduce their figures. This work was supported in part by NASA through grant #HF-1043 awarded by the Space Telescope Science Institute which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA under contract NAS5-26555, and by the Swiss National Science Foundation. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, Caltech, under contract with NASA.