Einstein predicted gravitational waves back in year 1916 but do they exist?
So far we have had no direct evidence for gravitational waves (except for some unconfirmed results) but we have had some indirect evidence which gives us hope.
In 1974, Russel Hulse and Joseph Taylor observed the motion of a binary pulsar. They saw that its period of rotation sped up at a rate that could only be explained by the emission of gravitational waves.
The search for direct evidence has gone on since the 1960s with "resonant-mass detectors" pioneered by Weber. These are basically large cylinders of metal that resonate if a gravitational wave passes through them at the resonant frequency. This method of gravitational wave detection does not look promising. It is limited by thermal and mechanical noise and will only detect gravitational waves perpendicular to its axis and with frequencies near the resonant frequency. There are proposed spherical resonant-mass detectors that will be able to detect gravitational waves in any direction, but the band-width of these detectors is still limited and therefore much time and money has been put into the detection of gravity waves using interferometers.