Automatic differentiation (AD) is a semantic transformation that applies the rules of differential calculus to source code. It thus transforms a computer program that computes a mathematical function into a program that computes the function and its derivatives. Derivatives play an important role in a variety of scientific computing applications, including optimization, solution of nonlinear equations, sensitivity analysis, and nonlinear inverse problems. This talk will contain an introduction to automatic differentiation, including a discussion of the forward and reverse modes for computing derivatives and various performance-enhancing strategies. I will also discuss the coupling of AD with numerical toolkits, such as the Toolkit for Advanced Optimization, and the use of AD tools in conjunction with NEOS solvers.