This article reviews the principles and applications of the phase field technique for modeling phase transformations and microstructural evolutions, with an emphasis on solid-solid transformations. Conventional phase field models, which rely on phenomenological thermodynamic and kinetic descriptions, are first presented and examples of application are discussed. Then, applications of the phase field method to phenomena induced by irradiation are reviewed, including radiation-enhanced and radiation-induced segregation and precipitation on sinks such as grain boundaries, dislocation and dislocation loops, the dynamical stabilization of compositional patterns and void lattices and the disordering of ordered precipitates.