We present some recent results concerning the homogenization of uniformly elliptic equations in nondivergence form. The equations are assumed to have coefficients which are independent at unit distance. We give optimal results on the order of the error in homogenization in every dimension, measured in L^\infty and Holder spaces up to C^{1,\alpha}, \alpha\leq 1. As a corollary, we obtain the existence of stationary correctors exist in dimensions five and higher (and their nonexistence, in general, in dimensions four and smaller). Finally, we give regularity results which state that a generic equation has essentially the same regularity as Laplace's equation, up to C^{1,1}.