The morphological scheme devised by Hubble and followers to classify galaxies has, over many decades, proved to be quite effective in directing our quest for the fundamental parameters describing the extragalactic manifold. This statement, however, is far more true for spirals than for ellipticals. In the last few years efforts have been made to search for a more meaningful classification of ellipticals, at the same time the classical question of whether E galaxies form a physically homogenous family has been brushed up once more. This book pictures the state of the art of this exciting transition process from the morphological to the physical `era' in the classification of galaxies.