It is now well established that both thunderclouds and lightning routinely emit x-rays and gamma-rays. These emissions appear over wide timescales, ranging from submicrosecond bursts of x-rays associated with lightning leaders, to sub-millisecond bursts of gamma-rays seen in space called terrestrial gamma-ray flashes, to minute long glows from thunderclouds seen on the ground and in or near the cloud by aircraft and balloons. In particular, terrestrial gamma-ray flashes (TGFs), which are thought to be emitted by thunderclouds, are so bright that they sometimes saturate detectors on spacecraft hundreds of kilometers away. These TGFs also generate energetic secondary electrons and positrons that are detected by spacecraft in the inner magnetosphere. It is generally believed that these x-ray and gamma-ray emissions are generated, via bremsstrahlung, by energetic runaway electrons that are accelerated by electric fields in the atmosphere. In this paper, we review this newly emerging field of High-Energy Atmospheric Physics, including the production of runaway electrons, the production and propagation of energetic radiation, and the effects of both on atmospheric electrodynamics.