We present new observational results on the kinematical, morphological, and stellar population properties of a sample of 21 dEs located both in the Virgo Cluster and in the field, which show that 52% of the dEs (1) are rotationally supported, (2) exhibit structural signs of typical rotating systems such as disks, bars, or spiral arms, (3) are younger (~3 Gyr) than non-rotating dEs, and (4) are preferentially located either in the outskirts of Virgo or in the field. This evidence is consistent with the idea that rotationally supported dwarfs are late-type spirals or irregulars that recently entered the cluster and lost their gas through a ram pressure stripping event, quenching their star formation and becoming dEs through passive evolution. We also find that all, but one, galaxies without photometric hints for hosting disks are pressure supported and are all situated in the inner regions of the cluster. This suggests a different evolution from the rotationally supported systems. Three different scenarios for these non-rotating galaxies are discussed (in situ formation, harassment, and ram pressure stripping).