Wave collapse is a formation of singularity arising in an initially smooth wave field due to nonlinearity. Self-focusing of light and breaking of seawaves are classical examples of such phenomena. Another conspicuous example is the collapse of Langmuir wave in plasma. This book offers a scientific systematic overview of the wave collapse theory. It includes a detailed theory of collapses in the framework of the nonlinear Schrodinger equation and its generalizations, and also applications to nonlinear optics and plasma physics. The theory of wave-breaking and vortex reconnection in hydrodynamics is also discussed.