In this paper, we prove that a wide class of distributed control problems subject to communication and propagation delays are equivalent to convex optimization problems. The results hold in both continuous and discrete time, for both stable and unstable systems. A specific example is formation flight, where each aircraft has its own controller, and the effects of an aircraft's control actions propagate to neighboring aircraft with a delay inversely proportional to the speed of sound. Here each controller may transmit sensor measurements from its aircraft to neighboring aircraft with an associated communication delay, and a consequence of these results is that if the communication delay is less than this propagation delay, then norm-optimal controllers may be found via convex programming.