dEs are frequently denoted as examples of "stellar fossile" systems in which the bulk of their SF occurred in the past. They are preferentially located in morphologically evolved environments , i.e. in regions with high galaxy densities and dominate the morphological types of galaxies in clusters, as e.g. Virgo, Coma, Fornax, and Perseus. Furthermore, dEs cluster strongly around luminous elliptical/S0 galaxies . The evolution of this galaxy type should be mainly caused by gas and tidal effects on SF and structure and indicates that it is strongly affected by environment.
Already  found that cluster dEs are usually almost free of interstellar gas and contain few young stars. In trying to understand the dE population, structural regularities and correlations must be studied, as it is known since the 80th, between optical surface brightness and luminosity [47, 20] and between luminosity and stellar velocity dispersion which also correlates with metallicity (e.g. ). Boselli et al.  proposed to understand these "Kormendy" relations by processes having transformed dIrrs after their cluster infall, but accuse the still existing lack of numerical simulations of such transformation.
Furthermore, dEs often have flattened profiles but are mostly kinematically supported by their stellar velocity dispersion rather than by rotation.
The combination of low gas-mass fractions and moderate-to-low stellar metallicities in dE (about 0.1 of solar or less) is a key feature of this class. Their lower stellar abundances  suggest that extensive gas loss occurred during their evolution and SF ceased due to a lack of raw material rather than exhaustion of the gas supply through SF. Galactic winds are therefore a hallmark of modern models for dE evolution, starting from the basic consideration by  and continued with the study by . They are commonly assumed to have cleaned out DGs soon after their formation. As mentioned in sect. 2, however, gas expulsion by means of galactic winds is inefficient from our understanding of the multi-phase ISM and requires even in low-mass systems a DM-to-baryonic matter ratio  much smaller than assigned to DGs in the classical formation picture (e.g. ).
There are two competing scenarios for the origin of cluster dEs. On the one hand, those low-mass galaxies are believed to constitute the building blocks in CDM cosmology and should therefore have evolved congruently with the mass accumulation to more massive entities, galaxies and galaxy clusters. For those, orbiting in a cluster the stellar component must be heated continuously by harrasment of more massive cluster galaxies and thus be pressure supported. On the other hand, a variety of observations are available which also support discrepant scenarios of dEs evolution. Recent Hi studies of Virgo cluster dEs  and also those of the Fornax cluster (see e.g. ) have unveiled that a small but significant fraction of them contains gas, has experienced recent SF, and can be argued from internal kinematics and cluster distribution data to represent an infalling class of different types of gas-rich galaxies in or after the state of morphological transformation. Further findings of a significant fraction of rotationally supported dEs in the Virgo cluster  and also disk features as e.g. spiral arms and bars  support the possibility of morphological transformation from gas-rich progenitor DGs to dEs thru gas exhaustion. Boselli et al.  have comprehensively discussed the different processes of dE origin.
A separation into dE subclasses with respect to their origin should also be visible in an intermediate-age stellar population, blue centers, and flatter figure shape. Indeed, dEs in the Virgo cluster can be divided into different subclasses  which differ significantly in their morphology and clustering properties, however, do not show any central clustering, but are distributed more like the late-type galaxies. These types of dEs show different disk signatures, such as bars and spiral structures, are not spheroidal, but rather thick disk-like galaxies. Similar shapes were also found for the brighter, non-nucleated dEs. There is only a small fraction of nucleated dEs whithout any disk features or cores, which keep the image of spheroidal objects consisting of old stars.
A figure analysis of Virgo dEs correlates with the averaged orbit velocity in the sense that flatter dEs show on average a larger orbital velocity (700 km/s) than those originating within the cluster (300 km/s)  (see Fig. 4). This kinematical dichotomy is expected because galaxies formed in virial equilibrium within the cluster retain their initial kinetic energy while the cluster mass grew. Galaxies falling into the present cluster potential must therefore possess larger velocities. To obtain information about both evolutionary stages, the young infalling vs. the late cluster members,  studied SDSS data. The basic model is that dIrrs which are formed outside the Virgo Cluster and becoming stripped on their infall, by this being transformed into dEs, should reveal properties recognizably different from dEs which have already aged in the cluster, as e.g. colors, effecitve radius, radial stellar distribution, and abundances. One result by  is that for the two dE populations, with and without cores, distinguished by their Sersic parameter, there is only a slight indication that non-nucleated dEs are more concentrated towards the inner cluster regions, whereas the fraction of nuclated dE is randomly distributed, while  found it to increase with distance. An analysis of the relation between the central surface brightness and the Sersic parameter shows the expected tendency to higher values for brighter galaxies. Furthermore, there were no further relations found of the Sersic parameter, the effective radius, or the distance from M 87.
Figure 4. Distribution of dEs in the Virgo Cluster divided into rapid (white) and slow objects (darker central part) overlaid with X-Ray brightness contours (courtesy by Thorsten Lisker).
Deeper insights are provided by spectra. Koleva et al.  found most dEs in the Fornax cluster to be roundish and to contain significant metallicity gradients already in the old stellar population. They argue that this is due to a lack of sufficient mixing. In contrast, rotationally supported dEs have flat metallicity distributions. Compared with simulations this can be attributed to galactic winds, but the picture of metallicity and gradients is not yet clear. While  show a tight positive correlation between the total metallicity [Z/H] and the mass,  do not find any trend involving [Fe/H] for Fornax-cluster and nearby-group dEs.
Moreover, from the deconvolution of the SF history of their sample dEs with respect to the central 1 arcmin and within the effective radius  draw the conclusions that for a few objects SF episodes occurred in the very center even within the last 1 Gyr. From a systematic study of the central Fornax-cluster dEs' dynamics  conclude that these objects stem from an infall population of late-type DGs and has been transformed to dEs by ram-pressure stripping (RPS).
Toloba et al.  derive for Coma cluster dEs to be weaker in carbon than dEs in low-density environments, while similar in nitrogen. Actually, they  also find that pressure supported Virgo dEs show higher dynamical mass-to-light ratios than rotationally supported dEs of similar luminosity and further that dEs in the outer parts of the cluster are mostly rotationally supported with disky shapes. Rotationally supported dEs even follow the Tully-Fisher relation. One fundamental and most spectacular result  is, however, that dEs are not DM-dominated galaxies, at least up to the half-light radius.
Correlations of both signatures, SF history and metallicity gradients, for cluster-member dEs vs. infall dEs should be derived for more clusters, but observations are unfortunately very time-expensive if possible at all.
In addition to classical dEs, ultra-compact DGs (UCDs) have been detected and classified as a new type of cluster dEs that differ by their intrinsic structure and brightness (see e.g. [75, 27]). The origin of these peculiar DGs is mysterious and not yet understood but requests transformation if they are surviving nuclei of tidally stripped nucleated DGs .