Preliminary specifications for the Square Kilometre Array (SKA) call for 25% of the total collecting area of the dish array to be located at distances greater than 180 km from the core, with a maximum baseline of at least 3000 km. The array will provide angular resolution θ ≲ 40–2 mas at 0.5–10 GHz with image sensitivity reaching ≲50 nJy beam−1 in an 8-hour integration with 500-MHz bandwidth. Given these specifications, the high-angular-resolution component of the SKA will be capable of detecting brightness temperatures ≲200K with milliarcsecond-scale angular resolution. The aim of this article is to bring together in one place a discussion of the broad range of new and important high-angular-resolution science that will be enabled by the SKA, and in doing so, address the merits of long baselines as part of the SKA. We highlight the fact that high angular resolution requiring baselines greater than 1000 km provides a rich science case with projects from many areas of astrophysics, including important contributions to key SKA science.