Space telescopes have the advantage of being above the blurring effects of the Earth's atmosphere. In addition, there are many wavelengths from the electromagnetic spectrum that do not reach Earth because they are absorbed or reflected by the Earth's atmosphere. In fact, as you can see from the diagram below, it is only the wavelengths of visible light, a small portion of infrared, and a part of the radio wavelengths that reach Earth at all. To observe ultraviolet, x-rays, gamma rays or infrared, astronomers have had to put telescopes outside of Earth's atmosphere -normally in orbit around the Earth.
Water vapor in the atmosphere absorbs much of the infrared radiation from space so the infrared observatories on Earth are located on high, dry mountains such as Mauna Kea in Hawaii. Even at high altitudes, however, the quality of observations in infrared is limited. The best solution for infrared observing is to put a telescope in orbit above the Earth and use radio to send data back to Earth. The Herschel Space Observatory was launched in May 2009 and the Spitzer Space Telescope was launched in August 2003. Herschel's primary mirror is 3.5 meters in diameter and the telescope is designed for infrared wavelengths from 55 to 672 µm. Spitzer's primary mirror is 0.85 meters across and it is designed for wavelengths of 3 to 180 µm. Infrared observatories in space must be kept very cold because otherwise infrared radiation from the telescope itself would interfere with its ability to observe infrared radiation from space. Spitzer exhausted its liquid helium coolant in 2009 and only a few of its instruments are still being used. Herschel's mission came to an end in 2013, when it also ran out of coolant.
Astronomers study the infrared wavelengths to study the early universe and to learn about objects that are too cold to generate visible light including brown dwarf stars and dust clouds.
Visible wavelengths make it through Earth's atmosphere, but turbulence in the atmosphere causes images of stars to be blurred and spread out by at least 0.5", even at the best observing sites in the world. The Hubble Space Telescope observes from an orbit about 559 km above the Earth at wavelengths from near infrared through the visible range and into the ultraviolet. It has a 2.4 meter primary mirror. It was put into orbit in 1990 and had a major repair in 1993. In May 2009 it was serviced again and should last until its successor, the James Webb Space Telescope (JWST), is launched in 2021. The JWST will be optimized for infrared observation, however, and ground based observatories will be the main source of observations in the visible range when Hubble is no longer able to operate. The Kepler Space Telescope was launched in March, 2009 and was active until November 2018. It had a 1.4 meter diameter primary mirror, and observed in the visible and infrared range of wavelengths. It had a very large field of view and was used to search for Earth sized planets within our galaxy. It detected 2,662 planets during its mission.
X-ray telescopes make it possible to study objects with temperatures between 106 and 108 K (between about 1 million and 100 million °C). When atoms in a gas are this hot, they move so fast that when they collide, they emit X-ray photons with wavelengths less than 10 nm. The Earth's atmosphere blocks all X-rays from space, so space telescopes must be used to observe in these wavelengths. X-rays have such high energy that the typical reflecting telescope design used for radio, infrared and optical telescopes cannot be used as the X-rays would just penetrate into the mirror. Instead, mirrors are arranged in specially shaped tubes so that the X-rays coming into the telescope just skim off the surface of the mirror (similar to skipping a stone on the surface of a lake) and onto a detector. Two X-ray telescopes currently in space are the Chandra X-ray Observatory and the XMM-Newton.
Gamma-ray telescopes such as the Fermi Gamma-ray Space Telescope do not use mirrors at all and instead have special detectors to measure the energy and direction of the most energetic electromagnetic radiation in the universe, gamma-rays. The Fermi Gamma-ray Space Telescope detects gamma-rays with energies from 10 keV to 300 GeV and has a very large field of view. It sees approximately 20% of the sky at once, and can cover the entire sky every three hours. Studying gamma-rays helps astronomers learn more about many things including active galactic nuclei, blazars, gamma-ray bursts, pulsars and solar flares.