The book provides a broad overview of the full spectrum of state-of-the-art computational activities in multiphase flow as presented by top practitioners in the field. Starting with well-established approaches (point-particle models, volume-of-fluid, level set, and front capturing for free-surface flows) it builds up to newer methods for large-eddy simulations, extended particles in Navier-Stokes flows, the lattice-Boltzmann method, molecular dynamics techniques and compressible flows with shock waves. These methods are illustrated with applications to a broad spectrum of problems involving particle dispersion and deposition, turbulence modulation, environmental flows, fluidized beds, bubbly flows, and many others.