  We give an overview of some recent results in hypersymplectic and
para-quaternionic Kahler geometry, and introduce the notion of split
three-Sasakian manifold. In particular, we discuss the twistor spaces and Swann
bundles of para-quaternionic Kahler manifolds. These are used to classify
examples with a fully homogeneous action of a semi-simple Lie group, and to
construct distinct para-quaternionic Kahler metrics from indefinite real
analytic conformal manifolds. We also indicate how the theory of toric
varieties gives rise to constructions of hypersymplectic manifolds.
