We present an implementation of Maxwell's equations that incorporates the spatially nonlocal response of materials, an effect necessary to describe the optical properties of structures with features less than 10 nm. For the first time it is possible to investigate the nonlocal optical response of structures without spherical or planar shape, and outside of the electrostatic limit. As an illustration, we calculate the optical properties of Au nanowires and show that nonlocal effects are particularly important in structures with apex features, even for arbitrarily large sizes.