Classical physics is thought to be local in the sense that no influences can travel faster than the speed of light, so what is done in one of two regions which are space-like separated (in the relativistic sense) cannot influence what goes on in the other. Claims have been made that quantum physics is, by contrast, nonlocal: either because of wave function collapse, or because quantum mechanics leads to results violating Bell's inequality. It will be argued that these claims are incorrect, and are based on a misunderstanding of how quantum mechanics differs from classical mechanics. \par While states can lack locality in a specifically quantum sense, the theory implies a principle of Einstein locality which excludes superluminal influences.