Gravitational waves are quadrupole oscillations of the classical gravitational field, that travel through space at the speed of light; they are generated by the rapid relative motion of two or more bound gravitating masses. They were proposed by Oliver Heaviside in 1893 and then later by Henri Poincaré in 1905 as the expected gravitational equivalent of electromagnetic radiation. In 1916, Albert Einstein demonstrated that gravitational radiation results from his 1915 field theory of gravity, as ripples in spacetime itself. Unlike electromagnetic radiation, which has a vector character and is generated by oscillating charge (a time-dependent dipole), gravitational radiation is of 2nd rank tensor character, and is generated by two or more masses in very close orbit around a common center of mass... a gravitational quadrupole. [If gravity could be quantized, the bosons would have spin 2.]

Heaviside (1850 – 1925)

Poincaré (1854 – 1912)

In later years various physicists, including Einstein himself, concluded that gravitational radiation could not do work and was therefore indetectable, or even nonexistent. Richard Feynman challenged that prevailing idea in a talk delivered in 1957, where he proposed a now famous thought experiment, the sticky bead, demonstrating conceptually that gravitational radiation could do work, and was therefore detectable. This revelation unfortunately inspired some crackpots who made absurd claims that they had detected such radiation, during the 1960s. However, it also inspired many physicists to think about what a realistic and practical gravitational wave telescope would look like, and precisely how it would work. A two-armed laser interferometer seemed to be the best bet.  Meanwhile, indirect detection was becoming possible.  A very close binary star system should be losing total energy via gravitational radiation, by a detectable amount. Indeed, the first indirect evidence for the existence of gravitational waves came in 1974 from the observed orbital decay of a binary neutron star system (binary pulsars), which matched the amount of decay, predicted by Einstein's theory of gravity, for energy lost by the system through emission of gravitational radiation. In 1993, Russell Alan Hulse and Joseph Hooton Taylor Jr. received the Nobel Prize in Physics for their discovery.

Feynman

Hulse and Taylor

The way to detect gravitational waves directly was, after much thought by many people, determined to be a two-armed laser interferometer. When a gravitational wave passes through the interferometer, vaguely speaking, one of the arms gets shorter and the other arm gets longer, and then vice versa, by an incredibly tiny amount. But with very powerful lasers, and multiple reflections of the beam to increase intensity, the interference due to these incredibly small distance changes is detectable... the change can be less than 10^-19 meters!  The actual detectors are nearly perfectly isolated pendulums, which are also mirrors. 

The first direct observation of gravitational waves was made in September 2015, when a signal generated by the merger of two black holes was received by the twin LIGO gravitational wave detectors in Livingston, Louisiana, and in Hanford, Washington. The 2017 Nobel Prize in Physics was subsequently awarded to Rainer Weiss, Kip Thorne and Barry Barish for their role in this at-last direct detection of gravitational waves.

Barish, Thorne and Weiss

The primary currently existing ground-based gravitational wave detectors are the two LIGO (Laser Interferometer Gravitational-Wave Observatory) installations, Virgo, and KAGRA (Kamioka Gravitational Wave Detector). LIGO has its twin detectors in the US, Virgo is located in Italy, and KAGRA is in Japan. In addition to these, there are smaller, more focused detectors, such as GEO600 in Germany. Because the length of the arms of the interferometer limit the wavelengths of gravitational radiation that can be observed, a multinational effort has been devoted to the development of interferometers consisting of multiple systems of satellites (usually three) in orbit about earth or sun.   Observations of events emitting strong pulses of gravitational radiation are now routine, and a huge library of black hole-black hole collisions and other collisions  (neutron star-black hole and neutron star-neutron star) that emit detectable gravitational radiation is being assembled.  Sensitivity of the existing detectors is constantly being improved.

Calculations of the aspects of black hole-black hole collisions are a big challenge to current physics, so that three totally different theoretical approaches are needed to deal with the three different stages of the single process!