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To understand the implications of migration for sustainable development requires a comprehensive consideration of a range of population movements and their feedback across space and time. This Perspective reviews emerging science at the interface of migration studies, demography, and sustainability, focusing on consequences of migration flows for nature-society interactions including on societal outcomes such as inequality; environmental causes and consequences of involuntary displacement; and processes of cultural convergence in sustainability practices in dynamic new populations. We advance a framework that demonstrates how migration outcomes result in identifiable consequences on resources, environmental burdens and well-being, and on innovation, adaptation, and challenges for sustainability governance. We elaborate the research frontiers of migration for sustainability science, explicitly integrating the full spectrum of regular migration decisions dominated by economic motives through to involuntary displacement due to social or environmental stresses. Migration can potentially contribute to sustainability transitions when it enhances well-being while not exacerbating structural inequalities or compound uneven burdens on environmental resources.