The standard model for describing propagation of a pulse-shaped complex field envelope in nonlinear dispersive media is the nonlinear Schrodinger (NLS) equation. In the context of nonlinear optics, the main assumption made when deriving the NLS equation from Maxwell's equations is that the pulse-width is large as compared to the period of the carrier frequency. When this assumption is no longer valid, i.e., for pulse duration of the order of a few cycles of the carrier, the evolution of such "short pulses" is better described by the so-called short-pulse equation (SPE). In this talk, we will survey the main properties of the SPE including solutions and integrability as well as some associated constraints and variant equations.