The phase-field method is a powerful tool for the analysis of microstructure evolution. A multi-phase-field model is developed to run computer simulations in different areas of materials science: The anisotropic growth of MFI zeolite-like crystallites on a smooth substrate into a hydrothermal solution constituting thin films, and the analysis of the behavior of magnetic shape memory alloys, a class of active smart martensitic materials that are used as components in actuators and dampers