“Modulation” or “Amplitude” equations are simplified equations that are believed to capture the essentials of the behavior of more complicated physical systems. Examples include the Korteweg-de Vries equation (KdV), the nonlinear Schroedinger equation (NLS) and Ginzburg-Landau equation. They arise in many different physical contexts and serve as prototypical examples or “normal forms” for a variety of nonlinear phenomena. This talk will focus on the derivation of the NLS equation as an approximation to describe the propagation of pulses in nonlinear optical fibers and will also discuss how one can derive rigorous estimates for the difference between the approximation given by the NLS equation and the true solution of the more complicated physical system. If time permits I will also discuss possible modulation equations for regimes in which the NLS approximation breaks down.