Interfacial and free surface flows are common phenomena in fluid dynamics, which appear in various natural and engineering processes. Surface tension dominant flows with large flow distortions, such as deformation and breakup of liquid particles and bursting and coalescence of gas bubbles, attract much attention of researchers. Due to the fact that these phenomena often occur on scales of space and time for which experimental methods, such as visualization techniques, are difficult and sometime impossible to perform, numerical simulation serves as a useful alternative to better understand such flows. The challenge arising in the numerical simulation of interfacial and free surface flows is the moving surface between two immiscible fluids with distinct physical properties, the shape, location and movement of which need to be identified and determined. The interface and flow field interact dynamically in the sense that the interface moves under the action of the flow field, and the flow field is affected by the position of the interface. When the surface tension force is dominant, the flow field is greatly dependent on the geometric properties of the surface such as the curvature and normal at the interface. In that case, accurate modeling of the surface tension force and representation of the interface are critical.