Natural history museums are unique spaces for interdisciplinary research and 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 can 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, such as in biomimetic design, and by contributing to solutions to climate change, global health and food security challenges. As institutions, they have long been incubators for cutting-edge research in biology while simultaneously providing core infrastructure for research on present and future societal needs. Here we explore how the intersection between pressing issues in environmental and human health and rapid technological innovation have reinforced the relevance of museum collections. We do this by providing examples as food for thought for both the broader academic community and museum scientists on the evolving role of museums. We also identify challenges to the realization of the full potential of natural history collections and the Global Museum to science and society and discuss the critical need to grow these collections. 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 growth. 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.