Low-luminosity elliptical galaxies are distinguished from late-type
galaxies (spirals and irregulars) by their smooth surface-brightness
profiles. Below luminosities of MB 
-18 the smooth-profile
galaxies divide into two classes: compact galaxies with high central
surface brightnesses (exemplified by M32), and diffuse galaxies with
low central surface brightnesses (exemplified by the Local Group dwarf
spheroidals). The terms ``dwarf elliptical'' (dE) and ``dwarf
spheroidal'' (dSph) have been used most often to describe smooth,
low surface brightness (LSB) galaxies. However, the lack of a universally
accepted definition has led to some confusion over whether these terms
refer to the same thing, and in particular whether the dE class
includes galaxies like M32. In the discussions that follow, we adopt the
classification scheme set out in the extensive
Virgo cluster dwarf atlas of
Sandage and
Binggeli (1984).
In this scheme the term dE encompasses both local dSph galaxies and
similar-looking galaxies beyond the Local Group.
Faint ellipticals with profiles
that are more nearly r1/4-law are referred to simply as
``ellipticals'' (E), or sometimes ``compact ellipticals,'' but never
dE's. A different name for ``dwarf elliptical'' frequently encountered in the
literature is ``spheroidal''. The pros and cons of either name convention are
discussed in
Binggeli (1994b) and
Kormendy and
Bender (1994).
More detailed issues of morphology, including the quantitative distinctions between the different classes and the existence of intermediate types, are discussed in Sect. 2.1.
All distance-dependent quantities discussed in this paper are
based on a long distance scale (H0 50 km s-1 Mpc-1),
although in most cases the distances are not estimated from
radial velocities.