In this talk we collect some estimates for the gradient of solutions, to the p-Laplace system with right-hand side in divergence form. Both estimates inside the domain for local solutions, and global estimates for solutions to boundary value problems are discussed, for Dirichlet boundary values. An outlook for generalizations is given. In that relation global estimates for the p-Stokes operator are presented. The talk covers joint works ion collaboration with: D. Breit, A. Cianchi, L. Diening, V. Macha and T. Kuusi.