Surface energy plays a major role in many phenomena that are important in technological and industrial processes, for example in wetting, grain growth and sintering. In this thesis, such surface-energy driven processes are studied by means of the phase-field method. The phase-field method is often used to model mesoscale microstructural evolution in materials. It is a diffuse interface method, i.e., it considers the surface or phase boundary between two bulk phases to have a non-zero width with a gradual variation in physical properties such as energy density, composition and crystalline structure. Neck formation and coarsening are two important diffusion-controlled features in solid-state sintering and are studied using our multiphase phase-field method. Inclusion of Navier-Stokes equation with surface-tension forces and convective phase-field equations into the model, enables simulation of reactive wetting and liquid-phase sintering. Analysis of a spreading liquid on a surface is investigated and is shown to follow the dynamics of a known hydrodynamic theory. Analysis of important capillary phenomena with wetting and motion of two particles connected by a liquid bridge are studied in view of important parameters such as contact angles and volume ratios between the liquid and solid particles. The interaction between solute atoms and migrating grain boundaries affects the rate of recrystallization and grain growth. The phenomena is studied using a phase-field method with a concentration dependent double-well potential over the phase boundary. We will show that with a simple phase-field model it is possible to model the dynamics of grain-boundary segregation to a stationary boundary as well as solute drag on a moving boundary. Another important issue in phase-field modeling has been to develop an effective coupling of the phase-field and CALPHAD methods. Such coulping makes use of CALPHAD's thermodynamic information with Gibbs energy function in the phase-field method. With the appropriate thermodynamic and kinetic information from CALPHAD databases, the phase-field method can predict mictrostructural evolution in multicomponent multiphase alloys. A phase-field model coupled with a TQ-interface available from Thermo-Calc is developed to study spinodal decomposition in FeCr, FeCrNi and TiC-ZrC alloys. / QC 20100622