  In this paper we study Fano threefolds with a torsion divisor
(Fano--Enriques). Due to this torsion divisor, they can be described as
quotients of Fano threefolds by a finite abelian group action. We start from
lists of Fano threefolds by Reid, Fletcher and Alt{\i}nok and check which of
them admit such an action with a Fano--Enriques quotient.
