Phase field models provide a well-established framework for the mathematical description of phase transitions on the meso scale. Allen-Cahn equations (non-conserved order parameter) and Cahn-Hilliard equations (conserved order parameter) are typical examples. In such classical phase field models the local interaction is approximated in terms of gradients of the order parameter. Recent non-local versions allow for far-field interaction replacing gradients by suitable integral operators. In spite of considerable progress concerning the analysis little is known about the efficient numerical solution of non-local phase field models. The goal of this project is to change that. Applications will particularly concentrate on the separation of binary and multicomponent alloys. However, the cooperation with other projects on semiconductor device simulation or image segmentation are envisaged as well.