Gravity as both fact and theory is one of the great success stories of the modern study of international trade, and has featured prominently in policy debates such as that over Brexit. We first review the facts, noting the overwhelming evidence that trade tends to fall with distance. We then introduce some expository tools for understanding CES theories of gravity as a simple general-equilibrium system. Next, we point out some anomalies with the theory, including implausible predictions for bilateral trade balances. Finally, we sketch an approach based on subconvex gravity as a promising direction to resolving them.