Is consciousness a continuous stream of percepts or is it discrete, occurring only at certain moments in time? This question has puzzled philosophers, psychologists, and neuroscientists for centuries. Both hypotheses have fallen repeatedly in and out of favor. Here, we review recent studies exploring long-lasting postdictive effects and show that the results favor a two-stage discrete model, in which substantial periods of continuous unconscious processing precede discrete conscious percepts. We propose that such a model marries the advantages of both continuous and discrete models and resolves centuries old debates about perception and consciousness.