Concepts are the building blocks of human cognition, linking what we perceive to past experiences, knowledge, theories, and imagination. Empirical studies have made progress on long-standing debates about concepts, including the following: Are there innate concepts? Do children’s concepts undergo qualitative changes? Do people’s concepts reflect the language(s) that they speak? And what are the roles of experience and expertise? These questions are all informed by studying children as well as adults, to provide insights into initial biases and processes of conceptual change. Concept formation has implications well beyond the laboratory, including social issues (including stereotyping, prejudice, and intergroup conflict), educational practices (including how intuitive biases stand in the way of learning scientific theories), and interacting with digital technologies and artificial intelligence. Ultimately, understanding concept formation requires contributions from multiple disciplines, methods, populations, and theoretical frameworks—including psychology, philosophy, and the cognitive sciences more broadly.