Over the past two decades, natural history collections (NHCs) have played an increasingly prominent role in global change research, but they have still greater potential, especially for the most diverse group of animals on Earth: insects. Here, we review the role of NHCs in advancing our understanding of the ecological and evolutionary responses of insects to recent global changes. Insect NHCs have helped document changes in insects' geographical distributions, phenology, phenotypic and genotypic traits over time periods up to a century. Recent work demonstrates the enormous potential of NHCs data for examining insect responses at multiple temporal, spatial and phylogenetic scales. Moving forward, insect NHCs offer unique opportunities to examine the morphological, chemical and genomic information in each specimen, thus advancing our understanding of the processes underlying species’ ecological and evolutionary responses to rapid, widespread global changes. This article is part of the theme issue ‘Biological collections for understanding biodiversity in the anthropocene’.