  We introduce a combinatorial characterization of simpliciality for
arrangements of hyperplanes. We then give a sharp upper bound for the number of
hyperplanes of such an arrangement in the projective plane over a finite field,
and present some series of arrangements related to the known arrangements in
characteristic zero. We further enumerate simplicial arrangements with given
symmetry groups. Finally, we determine all finite complex reflection groups
affording combinatorially simplicial arrangements. It turns out that
combinatorial simpliciality coincides with inductive freeness for finite
complex reflection groups except for the Shephard-Todd group $G_{31}$.
