Recent measurements of the extraterrestrial UV- and EUV-radiation, and the various theoretical approaches used in explaining the measured features of these radiations are reviewed. Whereas the structures and intensities of extraterrestrial EUV-radiation are essentially undetermined up to now, the observations of the extraterrestrial UV-sky give a clear indication of the existence of neutral interstellar hydrogen within the solar system. The effects of solar radiation pressure, and of temporal variations and spatial asymmetries in the solar radiations, on the structure of the extraterrestrial Lα sky are investigated in detail, and the various attempts to derive interstellar parameters from the interpretation of the measured Lα intensities are discussed. From these discussions the local interstellar medium is established as a tenuous hot intercloud H i-medium. The amount of its relative motion against the solar system cannot be reliably fixed. Further activities concerning the measurement of extraterrestrial UV- and EUV-radiation features are suggested that may be highly valuable in clarifying the outstanding problems.