This article considers a curiosity-driven approach to curating focused on material culture that visitors encounter in physical spaces. Drawing on research into historical curiosity cabinets, it explores how a contemporary notion of curiosity has been put into practice in the new breed of culturally enlightened museums exploring interdisciplinary approaches to medicine, health, life, and art. Based on an inaugural professorial address at Copenhagen University, it reflects on exhibition projects there and at the Wellcome Collection in London. Museums are institutional machines that generate social understanding from material things. Their physical spaces influence how we learn, think, and feel in public; their material collections feed our comprehension, imagination, and emotions; and induce attentive behavior in curators and visitors.