A key question in option pricing concerns how to incorporate information about the prices of existing, liquidly traded options into the prices of exotic options. Rather than trying to calibrate market prices to models, an alternative approach is to construct model-free bounds on the price of exotic options. These bounds are derived from arbitrages that may be constructed using relatively simple trading strategies in vanilla options, and their simplicity means that the bounds are generally valid for a wide class of models. This article discusses the construction of arbitrage bounds for a variety of classes of exotic options, and describes different techniques and approaches to the construction of such bounds. Particular examples include model-free bounds on the price of one-touch options, and pricing barrier options under the assumption of put–call symmetry.