  I present an overview of pulse propagation methods used in nonlinear optics,
covering both full-field and envelope-and-carrier methods. Both wideband and
narrowband cases are discussed. Three basic forms are considered -- those based
on (a) Maxwell's equations, (b) directional fields, and (c) the second order
wave equation. While Maxwell's equations simulators are the most general,
directional field methods can give significant computational and conceptual
advantages. Factorizations of the second order wave equation complete the set
by being the simplest to understand. One important conclusion is that that
envelope methods based on forward-only directional field propagation has made
the traditional envelope methods (such as the SVEA, and extensions) based on
the second order wave equation utterly redundant.
