We present Calderón-Zygmund results for solutions to elliptic and parabolic problems in nondivergence form with discontinuous coefficients and irregular obstacles. We shall also obtain Morrey regularity results for the Hessian of the solutions and Hölder continuity of the gradient of the solutions. The talk is based on the joint work with Sun-Sig Byun, Ki-Ahm Lee and Jinwan Park.