Quantum mechanics has been enormously successful in describing nature at the atomic level. Most physicists believe that it is in principle the “whole truth” about the world, even at the everyday level. Such a view leads to a severe problem: in certain circumstances. The most natural interpretation of the theory implies that no definite outcome of an experiment occurs until the act of “observation.” For many decades this problem was regarded as “merely philosophical.” It was thought to have no consequences testable in experiment, but this situation has now changed dramatically. Professor Leggett will discuss the problem, some popular “resolutions” of it, the current experimental situation, and prospects for the future.