We have already seen how nonparametric inference (e.g. about a density or regression function) is possible when our target of interest is smooth. The aim of this chapter is to explore nonparametric methods in a different context, namely where our target can be reasonably modelled using shape constraints, for example monotonicity, convexity or log-concavity. Such constraints are quite natural in many applications; moreover, in contrast to the smoothing methods we have encountered previously, it is often possible to propose methods that do not require the choice of any tuning parameters. Indeed, we show how simple approaches based on maximum likelihood or least squares can frequently be employed even in these infinite-dimensional settings.