Terrestrial gamma-ray flashes (TGFs) from Earth's upper atmosphere have been detected with the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) satellite. The gamma-ray spectra typically extend up to 10 to 20 megaelectron volts (MeV); a simple bremsstrahlung model suggests that most of the electrons that produce the gamma rays have energies on the order of 20 to 40 MeV. RHESSI detects 10 to 20 TGFs per month, corresponding to approximately 50 per day globally, perhaps many more if they are beamed. Both the frequency of occurrence and maximum photon energy are more than an order of magnitude higher than previously known for these events.