Procedures for synthesizing digital polycrystalline microstructures are illustrated, from either 2D statistical data or 3D deterministic data. Finite element meshes representing the digital microstructures are generated using anisotropic and adaptive mesh refinement close to the grain boundaries. Digital mechanical testing based on crystal plasticity theory provides an estimate of the spatial distribution of strain energy within the polycrystalline aggregate. The latter quantity is used as an input for modelling subsequent static recrystallization, grain boundary motion being described within a level set framework. The kinetic law for interface motion accounts for both the stored strain energy and the grain boundary energy. The possibility to include nucleation events within the level set framework is illustrated, as well as the evolving topology of the grain boundary network. The recrystallization model is tested in different configurations and compared to the Johnson-Mehl-Avrami- Kolmogorov (JMAK) theory.