Young children have sophisticated representations of their visual and linguistic environment. Where do these representations come from? How much knowledge arises through generic learning mechanisms applied to sensory data, and how much requires more substantive (possibly innate) inductive biases? We examine these questions by training neural networks solely on longitudinal data collected from a single child (Sullivan et al., 2020), consisting of egocentric video and audio streams. Our principal findings are as follows: 1) Based on visual only training, neural networks can acquire high-level visual features that are broadly useful across categorization and segmentation tasks. 2) Based on language only training, networks can acquire meaningful clusters of words and sentence-level syntactic sensitivity. 3) Based on paired visual and language training, networks can acquire word-referent mappings from tens of noisy examples and align their multi-modal conceptual systems. Taken together, our results show how sophisticated visual and linguistic representations can arise through data-driven learning applied to one child’s first-person experience.