The desire to predict discoveries—to have some idea, in advance, of what will be discovered, by whom, when, and where—pervades nearly all aspects of modern science, from individual scientists to publishers, from funding agencies to hiring committees. In this Essay, we survey the emerging and interdisciplinary field of the “science of science” and what it teaches us about the predictability of scientific discovery. We then discuss future opportunities for improving predictions derived from the science of science and its potential impact, positive and negative, on the scientific community.