Statistical learning is the process of identifying patterns of probabilistic co-occurrence among stimulus features, essential to our ability to perceive the world as predictable and stable. Research on auditory statistical learning has revealed that infants use statistical properties of linguistic input to discover structure, including sound patterns, words, and the beginnings of grammar, that may facilitate language acquisition. Previous research on visual statistical learning revealed abilities to discriminate probabilities in visual patterns, leading to claims of a domain-general learning device that is available early in life, perhaps at birth. More recent research, however, challenges this view. Visual statistical learning appears to be constrained by limits in infants' attention and memory, raising the possibility that statistical learning, like rule learning, may be best characterized as domain-specific. Implications for theories of cognitive development will be discussed.