Until the 1980s it was assumed that at long times the movement of animals and humans conforms to normal diffusion, as opposed to anomalous diffusion. The main reason for this expectation is the central limit theorem. We briefly discuss these ideas and present evidence that animals do not in general diffuse like particles performing Brownian motion. We review the Lévy flight foraging hypothesis. Finally, we discuss human diffusion and the remarkable colonization of Madagascar by Austronesians.