The discovery in the late 1990s that photonic crystal fibers could dramatically enhance supercontinuum generation—the generation by nonlinear processes in glass of a broadband spectrum that can approach white light—has led to revolutionary advances in optical frequency metrology, optical coherence tomography, spectroscopy, and numerous other applications. However, the underlying processes that lead to the spectral broadening are complex and have not been clearly understood. This article presents a unified discussion of the various nonlinear supercontinuum spectral broadening processes. The review is illustrated by numerical simulations that illustrate the supercontinuum generation characteristics for conditions covering the typical experimental parameter range. The discussion encompasses picosecond, nanosecond, and also continuous wave fields, with particular attention given to the femtosecond regime.