  We survey recent results about the Torelli question for
holomorphic-symplectic varieties. Following are the main topics. A Hodge
theoretic Torelli theorem. A study of the subgroup W, of the isometry group of
the weight 2 Hodge structure, generated by reflection with respect to
exceptional divisors. A description of the birational Kahler cone as a
fundamental domain for the W-action on the positive cone. A proof of a weak
version of Morrison's movable cone conjecture. A description of the moduli
spaces of polarized holomorphic symplectic varieties as monodromy quotients of
period domains of type IV.
