Sustainability spans environmental, societal and economic challenges, from climate change to healthcare and education. Robotics holds substantial promise for addressing these issues, yet current developments remain fragmented and lack a unifying framework. This fragmentation risks unintended consequences, including unequal access to technology and missed opportunities for broader impact. Here we advocate for a new discipline, Sustainability Robotics, structured around three guiding principles: robots should be minimally invasive, reducing disruption to ecosystems and socio-economic systems; universally accessible, extending benefits to underserved communities and extreme environments; and symbiotic, generating mutually beneficial outcomes for humans and nature. We define two complementary dimensions. The first, sustainable robot design, focuses on minimizing environmental impact through materials, energy and manufacturing. The second, robotic solutions for sustainability, leverages robotics to address environmental, social and economic challenges. By integrating perspectives from science, engineering, economics, ethics and policy, Sustainability Robotics provides a foundation for coordinated research, education and innovation. This framework aims to align robotics development with global sustainability goals, enabling more equitable and effective technological impact.