The gamma rays escaping from a planet can be used to map the concentrations of various elements in its surface. In a planet, the high‐energy particles in the galactic cosmic rays induce a cascade of particles that includes many neutrons. The &ggr; rays are made by nuclear excitations induced by these cosmic‐ray particles and their secondaries (especially neutron capture or inelastic‐scattering reactions) and by the decay of the naturally‐occurring radioelements. After a short history of planetary &ggr;‐ray spectroscopy and its applications, the &ggr;‐ray spectrometer planned for the Mars Observer mission is presented. Laboratory experiments that simulate the cosmic‐ray bombardments of planetary surfaces or measure cross sections for the production of &ggr; rays are reviewed. Theoretical calculations for the processes that make and transport neutrons and &ggr; rays are discussed. The emphasis here is on studies of Mars and on new ideas, concepts, and problems that have arisen over the last decade, such as Doppler broadening and peaks from neutron scattering with germanium nuclei in a high‐resolution &ggr;‐ray spectrometer.