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The future of humanity depends on whether or not we have a vision to guide our transition toward sustainability, on scales ranging from local landscapes to the planet as a whole. Sustainability science is at the core of this vision, and landscapes and regions represent a pivotal scale domain. The main objectives of this paper are: (1) to elucidate key definitions and concepts of sustainability, including the Brundtland definition, the triple bottom line, weak and strong sustainability, resilience, human well-being, and ecosystem services; (2) to examine key definitions and concepts of landscape sustainability, including those derived from general concepts and those developed for specific landscapes; and (3) to propose a framework for developing a science of landscape sustainability. Landscape sustainability is defined as the capacity of a landscape to consistently provide long-term, landscape-specific ecosystem services essential for maintaining and improving human well-being. Fundamentally, well-being is a journey, not a destination. Landscape sustainability science is a place-based, use-inspired science of understanding and improving the dynamic relationship between ecosystem services and human well-being in changing landscapes under uncertainties arising from internal feedbacks and external disturbances. While landscape sustainability science emphasizes place-based research on landscape and regional scales, significant between landscape interactions and hierarchical linkages to both finer and broader scales (or externalities) must not be ignored. To advance landscape sustainability science, spatially explicit methods are essential, especially experimental approaches that take advantage of designed landscapes and multi-scaled simulation models that couple the dynamics of landscape services (ecosystem services provided by multiple landscape elements in combination as emergent properties) and human well-being.