  We present the stellar population analysis of a sample of 12 dwarf elliptical
galaxies, observed with the SAURON integral field unit, using the full-spectrum
fitting method. We show that star formation histories (SFHs) resolved into two
populations can be recovered even within a limited wavelength range, provided
that high S/N data is used. We confirm that dEs have had complex SFHs, with
star formation extending to (more) recent epochs: for the majority of our
galaxies star formation activity was either still strong a few ($\lesssim$ 5)
Gyr ago or they experienced a secondary burst of star formation roughly at that
time. This latter possibility is in agreement with the proposed dE formation
scenario where tidal harassment drives the gas remaining in their progenitors
inwards and induces a star formation episode. For one of our field galaxies,
ID0918, we find a correlation between its stellar population and kinematic
properties, pointing to a possible merger origin of its kinematically-decoupled
core. One of our cluster objects, VCC1431, appears to be composed exclusively
of an old population ($\gtrsim$ 10-12 Gyr). Combining this with our earlier
dynamical results, we conclude that the galaxy was either ram-pressure stripped
early on in its evolution in a group environment and subsequently tidally
heated, or that it evolved in situ in the cluster's central parts, compact
enough to avoid tidal disruption. These are only two of the examples
illustrating the SFH richness of these objects confirmed with our data.
