Taubes has proved that the diffeomorphism invariants of 4–manifolds derived from the monopole equation of Seiberg and Witten are non–trivial for symplectic manifolds. This imposes strong restrictions on the topology of symplectic 4–manifolds. Going further, Taubes has shown that the Seiberg–Witten invariants can be calculated by counting pseudo–holomorphic curves in the sense of Gromov. The diffeomorphism invariance of the number of pseudo–holomorphic curves leads to ification results for symplectic structures on 4–manifolds.