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Einstein's happiest thought was his leap from the observation that a falling person feels no gravity to the realization that gravity might be equivalent to acceleration. It affects all bodies in the same way because it is a property of spacetime -- its curvature -- not a force propagating through spacetime (like electromagnetic or nuclear forces). When expressed in a way that is manifestly independent of the choice of coordinates, this idea became General Relativity. But the ground for what is now known as the "equivalence principle" was laid long before Einstein, affording a fascinating example of the growth of a scientific idea through the continuous interplay between theory and experiment. That story continues through the present era, with improved techniques and measurements, and in the new environment of space. Theoretically, equivalence is now understood to rank with Lorentz invariance as one of nature's most fundamental principles. Violations of equivalence are generically predicted by attempts to unify gravity with "non-geometrical" fundamental interactions, but there is no consensus on the form that these violations will take. Experimental tests of equivalence thus face the challenge of striving simultaneously for the highest possible sensitivity and diversity in test materials.