We construct adaptive confidence sets in isotonic and convex regression. In univariate isotonic regression, if the true parameter is piecewise constant with k pieces, then the Least-Squares estimator achieves a parametric rate of order k/n up to logarithmic factors. We construct honest confidence sets that adapt to the unknown number of pieces of the true parameter. The proposed confidence set enjoys uniform coverage over all non-decreasing functions. Furthermore, the squared diameter of the confidence set is of order k/n up to logarithmic factors, which is optimal in a minimax sense. In univariate convex regression, we construct a confidence set that enjoys uniform coverage and such that its diameter is of order q/n up to logarithmic factors, where q−1 is the number of changes of slope of the true regression function. We will also discuss application of the presented techniques to sparse linear regression.