Bayesian accounts of development posit that infants form predictions about the causes of sensory signals in their environment and select actions that resolve the largest amount of uncertainty. This paper considers how this approach to infant development can inform and unify insights from experimental research on early cognitive development and language acquisition. In order to establish whether infants’ early inferential abilities conform to the basic assumptions of a Bayesian approach to cognition, we first conduct a systematic review of experimental studies on infants’ ability to form predictions about probabilistic contingencies. These studies provide evidence that infants exhibit sensitivity to the probabilistic structure of their surrounding environment and recruit their own uncertainty to guide their exploration of information in the world. We then demonstrate how these Bayesian computational principles may apply in the context of language acquisition by conducting a second systematic review of experiments on the facilitative role of infants’ vocal production. These studies indicate that infants are more likely to produce and allocate attention to those speech sounds that best afford the opportunity to reduce prediction error over time. This paper demonstrates how Bayesian models of cognition can offer a unifying framework to advance the understanding of cognitive processes in early development. This framework not only gives a larger perspective to current findings, but also provides conceptual tools to enable investigation of infants’ individual trajectories of behavioural change.