The first "radio astronomer" was Karl Jansky, who studied mysterious radio interference he picked up with his antenna. The signal repeated every 23 hours and 56 minutes. He finally determined that it was caused by our Milky Way Galaxy. The signal is strongest at the center of the galaxy, in the constellation Sagittarius.
The Very Large Array (VLA) is a radio telescope system in New Mexico.
The James Webb Space Telescope (JWST) is a large, space telescope optimized for viewing in the infrared part of the spectrum, scheduled for launch in 2018. From the NASA website: "JWST will find the first galaxies that formed in the early Universe, connecting the Big Bang to our own Milky Way Galaxy. JWST will peer through dusty clouds to see stars forming planetary systems, connecting the Milky Way to our own Solar System. JWST's instruments will be designed to work primarily in the infrared range of the electromagnetic spectrum, with some capability in the visible range.
JWST will have a large mirror, 6.5 meters (21.3 feet) in diameter and a sunshield the size of a tennis court. Both the mirror and sunshade won't fit onto the rocket fully open, so both will fold up and open only once JWST is in outer space. JWST will reside in an orbit about 1.5 million km (1 million miles) from the Earth." http://www.jwst.nasa.gov/
Ultraviolet astronomy studies light with wavelengths just shorter than visible light. This wavelength region turns out to be particularly useful for studying atomic emissions from hydrogen and helium, the two most common gases in space (and in the Sun, and stars, and gas giant planets). Ultraviolet light does not reach the Earth's surface, so ultraviolet astronomy is done from satellites in space. Ultraviolet detectors function well on telescopes with conventional optics such as Hubble Space Telescope. Ultraviolet images from Hubble have dramatically revealed planetary auroras on Jupiter and Saturn from magnetospheric electrons striking atomic and molecular hydrogen in auroral zones at high latitudes on the planets.
X-rays are higher energy and shorter wavelength than UV. Astronomy in X-rays has specific challenges that do not affect other wavelengths. Earth's atmosphere is opaque to X-rays, which means that astronomy in this energy range can only be performed by space telescopes, high altitude balloons, or sounding rockets.