This chapter presents the overview of this book. The book begins by deriving a multi-order parameter model of solidification in the grand potential ensemble. with a grand potential functional formulated in terms of multiple chemical potentials and phases. It includes methods for making phase field simulations of solidification for quantitative applications through the addition of anti-trapping fluxes to the chemical potential equations in order to control the level of solute trapping and other spurious effects caused by diffuse interfaces. The book deals with the case of single-phase, polycrystalline multi-component solidification in the so-called local supersaturation limit of each chemical component. It discusses the thin interface limit of phase field models. The book examines the detailed effects of the interface width on the solidification kinetics of a rapidly solidifying phase field interface. It focuses on showing how to asymptotically map the phase field model's thin interface behaviour onto the continuous growth model of solidification.