  We have investigated the magnetoelectric and magnetodielectric response in
FeVO$_4$, which exhibits a change in magnetic structure coincident with
ferroelectric ordering at $T_{N2}$$\approx$15 K. Using symmetry considerations,
we construct a model for the possible magnetoelectric coupling in this system,
and present a discussion of the allowed spin structures in FeVO$_4$. Based on
this model, in which the spontaneous polarization is caused by a trilinear
spin-phonon interaction, we experimentally explore the magnetoelectric coupling
in FeVO$_4$ thin films through measurements of the electric field induced shift
of the multiferroic phase transition temperature, which exhibits an increase of
0.25 K in an applied field of 4 MV/m. The strong spin-charge coupling in \fvo\,
is also reflected in the significant magnetodielectric shift, which is present
in the paramagnetic phase due to a quartic spin-phonon interaction and shows a
marked enhancement with the onset of magnetic order which we attribute to the
trilinear spin-phonon interaction. We observe a clear magnetic field induced
dielectric anomaly at lower temperatures, distinct from the sharp peak
associated with the multiferroic transition, which we tentatively assign to a
spin reorientation cross-over. We also present a magnetoelectric phase diagram
for FeVO$_4$.
