When comet Hyakutake (C/1996 B2) encountered Earth in March 1996 at a minimum distance of only 15 million kilometers (40 times the distance of the moon), x-ray and extreme ultraviolet emission was discovered for the first time from a comet. The observations were performed with the astronomy satellites ROSAT and EUVE. A systematic search for x-rays from comets in archival data, obtained during the ROSAT all-sky survey in 1990/91, resulted in the discovery of x-ray emission from four additional comets. They were detected at seven occasions in total, when they were optically 300 to 30&hthinsp;000 times fainter than Hyakutake. These findings indicated that comets represent a new class of celestial x-ray sources. Subsequent detections of x-ray emission from additional comets with the satellites ROSAT, EUVE, and BeppoSAX confirmed this conclusion. The x-ray observations have obviously revealed the presence of a process in comets which had escaped attention until recently. This process is most likely charge exchange between highly charged heavy ions in the solar wind and cometary neutrals. The solar wind, a stream of particles continuously emitted from the sun with ≈ 400 km s−1, consists predominantly of protons, electrons, and alpha particles, but contains also a small fraction (≈0.1&percent;) of highly charged heavier ions, such asC6+,O6+,Ne8+,Si9+,Fe11+.When these ions capture electrons from the cometary gas, they attain highly excited states and radiate a large fraction of their excitation energy in the extreme ultraviolet and x-ray part of the spectrum. Charge exchange reproduces the intensity, the morphology and the spectrum of the observed x-ray emission from comets very well. ©1999 American Institute of Physics.