Albert Einsten published his monumental life's work, The General Theory of Relativity, in 1915. It had taken him ten years of intensive effort and was the single most outstanding intellectual achievement by any human being since Sir Isaac Newton's 17'th century Principia Mathematica. Ironically, it was General Relativity that overturned one of Newton's more famous scientific theories - the Universal Law of Gravitation.
Einstein had worked on the General Theory virtually non-stop since publishing The Special Theory of Relativity in 1905. The Special Theory dealt only with objects moving in a straight line and at a constant speed (or at rest), but the General Theory extended this to include any object in any space-time inertial reference, moving or accelerating in any manner whatsoever. In fact, it was a complete theory of Gravity and has become accepted as one of the two fundamental theories that describe everything in the universe as we know it (the other fundamental theory is that of Quantum Mechanics).
However, just like the Special Theory ten years before, the General Theory was met with a degree of scepticism by the scientific community. After all, the Universal Law of Gravitation, the work of the most respected scientist of all time (Isaac Newton) was not only being challenged but completely overturned! It was not until 1919 that General Relativity became widely accepted, after British physicist Arthur Eddington had confirmed some of the theory's predictions during observations of Venus transiting the Sun. Of course, this is how the scientific process should work - when a new theory appears its predictions must be experimentally checked ; the theory will survive only as long as no observation contradicts it.
Just recently a pair of stars about 7000 light years from Earth (that is a LONG way away, but in cosmic terms actually quite close) have been able to provide further proof of General Relativity's correctness. These two stars comprise a massive neutron star and a white dwarf, tightly coupled by gravity and orbiting each other every two and a half hours. The large mass of the neutron star and the proximity of its companion white dwarf provided an unprecedented opportunity to test for the effects of Gravitational Waves, a hitherto undetected prediction of General Relativity. In the extreme conditions of such a binary system, the orbits of the two stars will decay and gravitational waves should be emitted, carrying energy away. By measuring the time of arrival of the radio pulses from the rapidly-spinning neutron star over a long period, astronomers were able to determine the rate of orbital decay and the amount of gravitational radiation emitted.
The results were published in the 26 April 2013 edition of the journal Science and are consistent with the predictions of General Relativity.
Gravitational waves were not detected directly but the observations uncovered further evidence of their existence. There is now renewed hope that these elusive waves will eventually be found by using advanced instruments to study even more extreme cases of tightly-orbiting binary stars - neutron stars and black holes, pairs of which are predicted to spiral inward and end in a spectacularly violent collision. Sooner or later one of the last remaining unproven predictions of Albert Einstein's genius will either be confirmed or discarded ...
[Update] Gravitational waves were conclusively proven in September 2015 when minute ripples in the fabric of space-time were detected by the Laser Interferometer Gravitational Wave Observatory (LIGO). These waves were the result of two tightly-orbiting black holes 1.3 billion light years away colliding, perhaps the most violent event possible in the Universe. The two holes were estimated to be about 29 and 36 times the mass of the sun respectively, and during the collision 3 Solar masses of matter was converted into gravitational waves - a peak power output of 50 times that of the entire visible universe.
Amazingly, this discovery was made almost exactly 100 years after Albert Einstein published his General Theory of Relativity (in which gravitational waves were predicted). The data that was collected from the collision matched General Relativity's theoretical calculations to an uncannily accurate degree.