We confront predictions of the currently popular theories for dE formation and evolution with the observed position of dEs in $\log L_B$ vs. $\log \sigma$, $\log L_B$ vs. $\log R_{\rm e}$, $\log L_B$ vs. $\log I_{\rm e}$, and $\log R_{\rm e}$ vs. $\log I_{\rm e}$ diagrams and in the ($\log \sigma,\log R_{\rm e},\log I_{\rm e}$) parameter space in which bright and intermediate-luminosity elliptical galaxies and bulges of spirals define a Fundamental Plane (FP). We show that the dE sequences in the various univariate diagrams are disjunct from those traced by bright and intermediate-luminosity elliptical galaxies and bulges of spirals. It appears that semi-analytical models (SAMs) that incorporate quiescent star formation with an essentially $z$-independent star-formation efficiency, combined with post-merger starbursts and the dynamical response after supernova-driven gas-loss, are able to reproduce the position of the dEs in the various univariate and bivariate diagrams.
