Phase field theory treats the phases in materials as fields inside a material, as opposed to tracking the motions of interfaces during phase transformations. The interface sharpness is determined by a balance between bulk free energies and the square gradients of the fields. Treating phases as fields has advantages for the computational materials science of microstructural evolution, and some kinetic mechanisms are described. The different equations for the evolution of a conserved order parameter (e.g., composition) and a nonconserved order parameter (e.g., spin orientation) are discussed. The structure of an interface, especially its width, is analyzed for the typical case of an antiphase domain boundary. The Ginzburg–Landau equation is presented, and the effects of curvature on interface stability are discussed. Some aspects of the dynamics of domain growth are described.