The view that innovation is a key driver for sustainability is widely accepted among scholars, industry professionals, and government representatives. This is due to the fact that sustainable development is a pressing issue that requires immediate action and changes from governments, industry, and society as whole. This article reviews the literature on innovations that can lead to transformations in individuals, organizations, supply chains, and communities toward a sustainable future. Although many of the articles explored in this review report on existing urgent environmental and social issues, their findings, recommendations, and contributions are encouraging as we make progress toward a sustainable society through innovation and change. This article reviews the diversity of innovation for Sustainable Development in the literature, proposes a typology of such a phenomenon, provides an overview of key articles based on the primary subjects they address, and identifies a series of recommendations for the future development of the field. •This article proposes a typology of innovation for sustainable development.•An organization, supply chain, or community evolves on a sustainability trajectory.•These trajectories are the paths these entities take to become more sustainable.•Learning is a crucial element for these entities to pursue sustainable innovations.•Sustainable innovation improves entities' sustainability trajectories and performance.