Within the field of animal social learning, attention is shifting away from the question of whether non-human primates and other animals are capable of imitation and other types of social learning, to the question of how important social transmission is in natural populations. Network based diffusion analysis (NBDA) is a novel statistical method that has been developed to answer this question. NBDA infers social transmission if the order and time at which individuals acquire novel behaviour follows a social network.  In this talk, I will explain the logic behind NBDA, and illustrate the use of the method in two cases. The first is a recent high profile case showing strong evidence for the social transmission of a novel feeding behaviour (lobtail feeding) among a wild population of humpback whales. The second is the application of NBDA to the spread of two novel behaviour patterns through the Sonso chimpanzee community. In the latter case, one behaviour pattern (moss-sponging) is shown to be socially transmitted, whereas the other (leaf-sponge re-use) is shown to be primarily asocially learned.