  This article is an overview of the results obtained in recent years on
symplectic connections. We present what is known about preferred connections
(critical points of a variational principle). The class of Ricci-type
connections (for which the curvature is entirely determined by the Ricci
tensor) is described in detail, as well as its far reaching generalization to
special connections. A twistorial construction shows a relation between
Ricci-type connections and complex geometry. We give a construction of
Ricci-flat symplectic connections. We end up by presenting, through an explicit
example, an approach to noncommutative symplectic symmetric spaces.
