  By a special symplectic connection we mean a torsion free connection which is
either the Levi-Civita connection of a Bochner-K\"ahler metric of arbitrary
signature, a Bochner-bi-Lagrangian connection, a connection of Ricci type or a
connection with special symplectic holonomy. A manifold or orbifold with such a
connection is called special symplectic.
  We show that the symplectic reduction of (an open cell of) a parabolic
contact manifold by a symmetry vector field is special symplectic in a
canonical way. Moreover, we show that any special symplectic manifold or
orbifold is locally equivalent to one of these symplectic reductions.
  As a consequence, we are able to prove a number of global properties,
including a classification in the compact simply connected case.
