Description of the cover page: The cover page shows pattern-formation during a spinodal decomposition of binary alloy in 3D, two and three-phase cross-sections of three-dimensional directionally solidified microstructures, morphological instabilities during dendritic and two-phase colony formation and finally the break-up of a thin-film as a result of a mechanical instability. These are some of the mechanisms of microstructural evolution which have been modelled using the phase-field method, and a respective description of the different applicable models form a part of this review.