Numerical methods for drops and bubbles have undergone impressive progress in recent years. So much so that it is now possible to compute the flow and deformation of thousands of individual bubbles in complex three-dimensional flows. This new book begins by outlining the underlying theory about drops, bubbles and interfaces. In particular the governing Euler and Navier-Stokes equations are covered, the resulting vorticity dynamics described and the regarding mass and heat transport are addressed. The monograph continues, detailing a catalogue of computational techniques for such problems including both fixed and adaptive approaches. The authors present a definitive account of state of the art methods in this emerging area of research, making this a standard text for researchers in the area of two-phase flow.