The ability to utilize the lunar surface as an observing site presents many opportunities for X‐ray and gamma‐ray astronomy in the early decades of the 21st century. Some of the advantages of a lunar base for certain instruments include the lack of an overlying atmosphere, the availability of stable real estate to establish instruments requiring large structures and long baselines, and ultimately the possibility of manufacturing and assembling extensive modular detection systems. X‐ray astronomy beyond 2010 will require detector systems with high angular resolution, large area collectors for high throughput, X‐ray cameras for all sky monitoring and hard X‐ray telescopes with long focal length, among other capabilities. Systems meeting these requirements which can be appropriately placed on the moon are discussed here. In the gamma‐ray range, the lunar surface seems appropriate for observation of transient phenomena at all wavelengths, high sensitivity spectroscopy of nuclear gamma‐rays, and possibly for implementation of the massive detector systems required for further advances in the 100 MeV, GeV, and TeV energy ranges.