The dwarf elliptical galaxies (dEs) are more luminous than dwarf spheroidals and fainter than "normal" ellipticals. In this paper I investigate the interconnection between these three families of early-type galaxies by studying their stellar populations properties. Some dwarf ellipticals have strong metallicity and age gradients, up to - 0.5 dex and 0.2 dex per decade of radius, respectively. The dispersion of the gradients is similar to the one observed in the dwarf spheroidals and normal ellipticals and there is no gradient-luminosity relation. The star formation history of dEs is characterised by a mass-dominant old population, generally prolonged to intermediate ages. This pattern is apparently independent of the environment (scarce groups or dense clusters), as confirmed by the observations of the Local Group dwarf spheroidals. At higher masses, the S0s have a similar star formation history, while the tail of late star formation is rarer and shorter in elliptical galaxies (MB ~ -19). I conclude that the transition between different classes is smooth, without any abrupt changes in their stellar population properties.