Studying human infants will increase our understanding of the nature, origins and function of neural mirroring mechanisms. Human infants are prolific imitators. Infant imitation indicates observation–execution linkages in the brain prior to language and protracted learning. Investigations of neural aspects of these linkages in human infants have focused on the sensorimotor mu rhythm in the electroencephalogram, which occurs in the alpha frequency range over central electrode sites. Recent results show that the infant mu rhythm is desynchronized during action execution as well as action observation. Current work is elucidating properties of the infant mu rhythm and how it may relate to prelinguistic action processing and social understanding. Here, we consider this neuroscience research in relation to developmental psychological theory, particularly the ‘Like-Me’ framework, which holds that one of the chief cognitive tasks of the human infant is to map the similarity between self and other. We elucidate the value of integrating neuroscience findings with behavioural studies of infant imitation, and the reciprocal benefit of examining mirroring mechanisms from an ontogenetic perspective.