Almost all early cognitive development takes place in social contexts. At the moment, however, we understand little about the neural and cognitive mechanisms that drive infant attention during social interactions. Recording EEG during naturalistic caregiver-infant interactions (N=66), we compare two different accounts. Attentional scaffolding perspectives emphasise the role of the caregiver in structuring the interaction, whilst active learning models focus on motivational factors, endogenous to the infant, that guide their attention. Our results show that, already by 12 months, intrinsic cognitive processes control infant attention: fluctuations in endogenous oscillatory neural activity associated with changes in infant attentiveness, and predicted the length of infant attention episodes towards objects. In comparison, infant attention was not forwards-predicted by caregiver gaze, or modulations in the spectral and temporal properties of the caregiver's speech. Instead, caregivers rapidly modulated their behaviours in response to changes in infant attention and cognitive engagement, and greater reactive changes associated with longer infant attention. Our findings suggest that shared attention develops through interactive by asymmetric, infant-led processes that operate across the caregiver-child dyad.