We present the first large-scale stellar kinematic and line-strength maps for dwarf elliptical galaxies (nine in the Virgo cluster and three in the field environment) obtained with the SAURON (Spectrographic Areal Unit for Research on Optical Nebulae) integral-field unit. No two galaxies in our sample are alike: we see that the level of rotation is not tied to flattening (we have, e.g., round rotators and flattened non-rotators); we observe kinematic twists in one Virgo and one field object; we discover large-scale kinematically decoupled components in two field galaxies; we see varying gradients in line-strength maps, from nearly flat to strongly peaked in the centre. The great variety of morphological, kinematic and stellar population parameters seen in our data points to a formation scenario in which properties are shaped stochastically. A combined effect of ram-pressure stripping and galaxy harassment is the most probable explanation. We show the need for a comprehensive analysis of kinematic, dynamical and stellar population properties which will enable us to place dwarf ellipticals and processes that govern their evolution in the wider context of galaxy formation.