Predicting the microstructure of materials is of paramount importance, as many properties of interest depend directly on the microstructure. Thus the overarching goal of the project is to predict the microstructure with the phase-field method, which allows for direct 4D (3D+time) observation of the microstructure. The simulations shed light on the mechanisms of microstructure evolution and allow the prediction of the evolution under a change of processing conditions as well as changes of the material itself. The processes of solidification and sintering are investigated in this project. Alloy solidification, specifically the coupled growth of dendrites and eutectics, forms one part of the work on the solidifcation, with the freeze-casting process as a preprocessing step for sintering forming the other. The main topic of sintering is investigated by employing not only phase-field methods but also molecular dynamics simulations. By combining results from both methods, it was possible to construct the first phase-field model which correctly accounts for the densification evolution of large three-dimensional packings. This model is then used to investigate the competing processes of grain growth and densification. Furthermore, the colloidal structure produced during freeze-casting is also computationally sintered with the method and thus represents the first simulation series of the freeze-casting process starting from a suspension and finishing with a porous, sintered structure.