(joint work with R.L. Fernandes, preprint, 2001)
In this survey we discuss the symplectic integration of Poisson manifolds. This discussion is motivated by the recent solution to the integrability problem for general Lie algebroids given in \cite{CrFe}, which we consider here for the special case of Poisson manifolds. In particular,
- we explain in detail how the Poisson sigma-model of Cattaneo and Felder relates to our approach,
- we show that a regular Poisson manifold is integrable iff its structure groupoid is a Lie groupoid,
- we discuss in more detail the monodromy groups of Poisson manifolds, which, appart from playing a central role in describing the obstruction to integrability, are interesting (Morita) invariants associated to (not necessarily integrable) Poisson manifolds.