Natural history museums are unique spaces for interdisciplinary research and for educational innovation. Through extensive exhibits and public programming and by hosting rich communities of amateurs, students, and researchers at all stages of their careers, they provide a place-based window to focus on integration of science and discovery, as well as a locus for community engagement. At the same time, like a synthesis radio telescope, when joined together through emerging digital resources, the global community of museums (the ‘Global Museum’) is more than the sum of its parts, allowing insights and answers to diverse biological, environmental, and societal questions at the global scale, across eons of time, and spanning vast diversity across the Tree of Life. We argue that, whereas natural history collections and museums began with a focus on describing the diversity and peculiarities of species on Earth, they are now increasingly leveraged in new ways that significantly expand their impact and relevance. These new directions include the possibility to ask new, often interdisciplinary questions in basic and applied science; inform biomimetic design; and even provide solutions to climate change, global health and food security challenges. As institutions, they are incubators for cutting-edge research in biology and simultaneously protect core infrastructure for present and future societal needs. In this perspective, we discuss challenges to the realization of the full potential of natural history collections and museums to serve society. After reviewing collections and types of museums, including local and global efforts, we discuss the value of specimens and the importance of observations. We then focus on mapping and modelling of museum data (including place-based approaches and discovery), and explore the main projects, platforms and databases enabling this. We also explore ways in which improved infrastructure will allow higher quality science and increased opportunities for interdisciplinary research and communication, as well as new uses of collections. Finally, we aim to improve relevant protocols for the long-term storage of specimens and tissues, ensuring proper connection with tomorrow’s technologies and hence further increasing the relevance of natural history museums.