  This review is dedicated to recent progress in the field of classical,
interacting, massive spin-2 theories, with a focus on ghost-free bimetric
theory. We will outline its history and its development as a nontrivial
extension and generalisation of nonlinear massive gravity. We present a
detailed discussion of the consistency proofs of both theories, before we
review Einstein solutions to the bimetric equations of motion in vacuum as well
as the resulting mass spectrum. We introduce couplings to matter and then
discuss the general relativity and massive gravity limits of bimetric theory,
which correspond to decoupling the massive or the massless spin-2 field from
the matter sector, respectively. More general classical solutions are reviewed
and the present status of bimetric cosmology is summarised. An interesting
corner in the bimetric parameter space which could potentially give rise to a
nonlinear theory for partially massless spin-2 fields is also discussed.
Relations to higher-curvature theories of gravity are explained and finally we
give an overview of possible extensions of the theory and review its
formulation in terms of vielbeins.
