As mentioned briefly on the page about optical observatories, ground-based optical telescopes can observe up to near-UV wavelengths, where the atmosphere starts cutting off incoming radiation. To observe at yet shorter wavelengths, one needs telescopes outside the Earth's atmosphere (or very high up, e.g. onboard a balloon).
The UV wavelength regime is considered to be diagnostically very important, because here one can observe - amongst other important objects - a plethora of emission lines from hot gas (around a few hundred thousand Kelvin), such as that in our Galaxy and the emission from hot massive stars (see the page on UV astronomy). There have been a number of UV satellite missions over the last decades.