  Let $\mathcal{A} = \mathcal{A}(W)$ be the reflection arrangement of the
finite complex reflection group $W$. By Terao's famous theorem, the arrangement
$\mathcal{A}$ is free. In this paper we classify all reflection arrangements
which belong to the smaller class of recursively free arrangements. Moreover
for the case that $W$ admits an irreducible factor isomorphic to $G_{31}$ we
obtain a new (computer free) proof for the non-inductive freeness of
$\mathcal{A}(W)$. Since our classification implies the non-recursive freeness
of the reflection arrangement $\mathcal{A}(G_{31})$, we can prove a conjecture
by Abe about the new class of divisionally free arrangements which he recently
introduced.
