Codimension one symplectic foliations (or, equivalently, corank one Poisson structures) are the Poisson counterparts of codimension one foliations. The added symplectic structures along the leaves makes them much harder to find (e.g. we still do not know whether they exist on the spheres of dimension greater than 5), but also more suitable for extending results from foliation theory (e.g. the confolations of Eliashberg-Thurston ) that work well in 3 dimensions (when the leaves are implicitly symplectic, via the area form).

In this talk I will describe some general constructions that allow one to produce such symplectic foliations. Some of these constructions originate from Mitsumatsu's construction on the 5-sphere as we understood them (discussions with I. Marcut), some are inspired by constructions from contact geometry (discussions with L. Toussaint) and the most recent ones are based on the relationship with (stable) generalised complex structures- joint work with G. Cavalcanti.