I study the computational basis of human learning and inference. Through a combination of mathematical modeling, computer simulation, and behavioral experiments, I try to uncover the logic behind our everyday inductive leaps: constructing perceptual representations, separating "style" and "content" in perception, learning concepts and words, judging similarity or representativeness, inferring causal connections, noticing coincidences, predicting the future. I approach these topics with a range of empirical methods -- primarily, behavioral testing of adults, children, and machines -- and formal tools -- drawn chiefly from Bayesian statistics and probability theory, but also from geometry, graph theory, and linear algebra. My work is driven by the complementary goals of trying to achieve a better understanding of human learning in computational terms and trying to build computational systems that come closer to the capacities of human learners.