Model-predictive control (MPC) is an increasingly popular method for controlling complex robotic systems in which optimal control problems are solved on board the robot at real-time rates. However, successful application of MPC depends critically on the performance of the algorithms used to solve the underlying optimization problems. An ideal solver should both leverage the structure of the MPC problem and support efficient "warm starting" so that information from previous solutions can be recycled to speed convergence. We present ALTRO-C, a high-performance solver with both of these properties that utilizes an augmented Lagrangian method to handle general convex conic constraints. We demonstrate the new solver’s superior performance against several existing state-of-the-art solvers on a variety of benchmark control problems formulated as both quadratic and second-order cone programs.