The nonlinear Schrödinger equation (NLS) arises in various areas of physics. In hydrodynamics, it describes the dynamics of surface gravity waves in finite or infinite depth. In optics, the NLS equation is a universal equation governing the evolution of slowly varying packets of quasi-monochromatic waves in weakly nonlinear media featuring dispersion, such as optical fibers and planar waveguides. In plasmas, the NLS equation arises in the adiabatic limit of Zakharov system describing Langmuir and ion-acoustic waves. The NLS equation is integrable and has a rich set of exact solutions, including solitons (exponentially localized pulses) and spatially uniform solutions (continuous waves). Although the NLS equation is just an approximation, its solutions describe experimental data remarkably well.