Basic Framework -- The Physical Context -- Structural Properties -- Rigorous Theory -- Existence and Long-Time Behavior -- Standing Wave Solutions -- Blowup Solutions -- Asymptotic Analysis near Collapse -- Numerical Observations -- Supercritical Collapse -- Critical Collapse -- Perturbations of Focusing NLS -- Coupling to a Mean Field -- Mean Field Generation -- Gravity-Capillary Surface Waves -- The Davey-Stewartson System -- Coupling to Acoustic Waves -- Langmuir Oscillations -- The Scalar Model -- Progressive Waves in Plasmas.