Sustainability has become a key concept of social change, associated with various visions – whether it's a green capitalism based on ecological modernization or a socio-ecological transformation that could herald a post-capitalist era. In this programmatic paper by Sighard Neckel and his research team in Hamburg, the social dimensions of sustainability are highlighted, as well as the paradoxes associated with sustainable development in global capitalism. Fundamental sociological perspectives on sustainability are discussed, along with insights into specific areas of critical-reflexive social research concerning the societal conflicts surrounding sustainability.