I will describe methods for multivariate nonparametric estimation based on constraining mixed partial derivatives. The resulting estimators are efficiently computable and work well in practice. They are also theoretically attractive when the underlying assumptions are satisfied, achieving rates of convergence that avoid the usual curse of dimensionality. Specific examples of this methodology include: MARS via LASSO, totally convex regression, Hardy-Krause variation constrained regression, and Entirely Monotonic Regression. Most of this presentation is based on joint work with Dohyeong Ki (UC Berkeley).