Quantum mechanics has been enormously successful in describing nature at the atomic level, and most physicists believe that it is in principle the "whole truth" about the world even at the every-day level. However, such a view prima facie leads to a severe problem: in certain circumstances, the most natural inter-pretationof 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", in the sense that it was thought that it had no consequences, which could be tested in experiment. However, the situation has changed dramatically in this respect in the last dozen or so years. I will discuss the problem, some popular "resolutions" of it, the current experimental situation, and prospects for the future.