Pointwise estimates for the gradient of solutions to the p-Laplace system with righthand side in divergence form are established. Their formulation involves the sharp maximal operator, whose properties enable us to develop a nonlinear counterpart of the classical Calderón–Zygmund theory for the Laplacian. As a consequence, a flexible, comprehensive approach to gradient bounds for the p-Laplace system for a broad class of norms is derived. The relevant gradient bounds are just reduced to norm inequalities for a classical operator of harmonic analysis. In particular, new gradient estimates are exhibited which augment the available literature in the elliptic regularity theory.