Einstein called his insight that gravitation is equivalent to an acceleration of the observer his “happiest idea.” This idea forms the basis of the modern relativistic theory of gravity in which gravity is not a conventional force but rather a manifestation of curved space-time. I will review the history of experimental tests of this profound “Equivalence Principle” and discuss the evolving motivations for improving such tests, which have now reached a precision of 2 parts in 10 trillion. Naturally, results of this extraordinary precision require clever experimental techniques. I will discuss the strategies of recent experiments, present their results and point out their relevance for antimatter and dark matter. The story illustrates how profound ideas develop, how incorrect experimental conclusions can stimulate new insights, and how the best experimental techniques are sometimes the least obvious.