The properties of dwarf galaxies are central to two current issues in observational cosmology: understanding the results from deep redshift surveys, and interpreting the constraints of the galaxy luminosity function on the primordial fluctuation spectrum. Deep redshift surveys have revealed a dominant population of star-forming dwarf galaxies at redshifts (0.2 < z < 0.5) (Broadhurst et al. 1988; Colles et al. 1990; Cowie et al. 1991). A large dwarf population is expected from simulations of galaxy evolution (White and Frenk 1991) based on the Cold-Dark-Matter (CDM) model. However, both the redshift surveys and the theory predict far more dwarfs than are observed locally. This puzzle points to a need to understand better the physics of dwarf galaxies.
The last decade has seen a surge of activity in the study of dwarf galaxies, inspired in part by such cosmological issues, but more directly by the availability of new technology: wide-field imaging telescopes and good photographic emulsions, CCD's, and sensitive spectrographs. This activity has resulted in major advances in our knowledge of the internal structure and kinematics, stellar populations, clustering properties, luminosity function, and evolution of dwarf galaxies. Our aim in this review is to examine some of the recent data with the cosmological issues in mind: do current observations of dwarf galaxies really constrain the theories? What future observations are most relevant to testing the models of galaxy evolution? To make the subject tractable, we have chosen to concentrate on dwarf elliptical (dE) galaxies, linking together both Local Group satellite dE's and the large dE populations of nearby clusters, and examining the data critically to try to decide what we know and what we only think we know about these galaxies. We will mention only in passing star-forming dwarf galaxies such as Magellanic irregulars or blue compact dwarf galaxies. Excellent reviews of the properties of these galaxies can be found in Kunth et al. (1986), Hunter and Gallagher (1989), and Meylan and Prugniel (1994).