During the last decade, direct numerical simulations of multiphase flow have emerged as a major research tool. It is now possible, for example, to simulate the motion of several hundred bubbles and particles in simple flows and to obtain meaningful average quantities that can be compared with experimental results. These systems are, however, still very simple compared to those systems routinely encountered in engineering applications. It is, in particular, frequently necessary to account for phase change, both between solid and liquid as well as liquid and vapor. Most materials used for manmade artifacts are processed as liquids at some stage, for example, and the way solidification takes place generally has major impact on the properties of the final product. The formation of microstructures, where some parts of the melt solidify faster than others, or solidify with different composition as in the case of binary alloys, is particularly important since the size and composition of the microstructure impact the hardness and ductility, for example, of the final product. Boiling is one of the most efficient ways of removing heat from a solid surface. It is therefore commonly used in energy generation and refrigeration. The large volume change and the high temperatures involved can make the consequences of design or operational errors catastrophic and accurate predictions are highly desirable. The change of phase from liquid to vapor and vice-versa usually takes place in a highly unsteady manner with a very convoluted phase boundary. Numerical simulations are therefore essential for theoretical investigations and while a few simulations of both problems have been published, the field is still very immature. In the talk the author gives a brief overview of the state of the art and discusses recent simulations of boiling and solidification in some detail.