Our best available theory of gravity, Einstein's general theory of relativity, was published in 1915. Field equations of the theory appear to have wave-like solutions, and therefore represent a potentially important prediction of the theory. However, for some decades it was not clear whether these mathematical solutions had physical meaning. Moreover, even if the waves were taken as physically real it was not clear that they could possibly be detected. A century elapsed before the exquisitely sensitive instrument known as LIGO first detected gravitational waves. Necessary steps along the way to discovery make a fascinating story -- one filled with blind alleys as well as successes. It's a superb example of the scientific method at work. I will discuss some of the necessary steps and a few of the failures.