Young children develop sophisticated internal models of the world based on their egocentric visual experience. How much of this is driven by innate constraints and how much is driven by their experience? To investigate these questions, we train state-of-the-art neural networks on a realistic proxy of a child's visual experience without any explicit supervision or domain-specific inductive biases. Specifically, we train both embedding models and generative models on 200 hours of headcam video from a single child collected over two years. We train a total of 72 different models, exploring a range of model architectures and self-supervised learning algorithms, and comprehensively evaluate their performance in downstream tasks. The best embedding models perform at 70% of a highly performant ImageNet-trained model on average. They also learn broad semantic categories without any labeled examples and learn to localize semantic categories in an image without any location supervision. However, these models are less object-centric and more background-sensitive than comparable ImageNet-trained models. Generative models trained with the same data successfully extrapolate simple properties of partially masked objects, such as their texture, color, orientation, and rough outline, but struggle with finer object details. We replicate our experiments with two other children and find very similar results. Broadly useful high-level visual representations are thus robustly learnable from a representative sample of a child's visual experience without strong inductive biases.