Assuming ‘ceteris paribus’ in terms of the viability of the planet during the coming half-century or so, the rising needs of a burgeoning, but also increasingly rich and demanding world population will drastically change agriculture. Crop yields and animal productivity will have to increase substantially, with the risk of further depleting the resource base and degrading the environment, making food production both the culprit and the victim. Future food security therefore depends on development of technologies that increase the efficiency of resource use and prevent externalization of costs. The current trend is towards intensification, especially more output per production unit so as to increase input efficiency. Whether that trend is sustainable is a matter of strong debate among scientists and policy-makers alike. The big question is how to produce more food with much fewer resources. Sustainable intensification (i.e., increasing agricultural output while keeping the ecological footprint as small as possible) for some is an oxymoron, unless real progress can be made in ecological intensification, that is, increasing agricultural output by capitalizing on ecological processes in agro-ecosystems. Definitions of intensification and sustainability vary greatly. The way these concepts are being used in different disciplines causes tensions and hides trade-offs instead of making them explicit. Inter-disciplinarity and boundary-crossing in terminology and concepts are needed. Implicitly, the operationalization of intensification and sustainability implies appreciation of and choices for values, an issue that is often overlooked and sometimes even denied in the natural sciences. The multidimensional nature of intensification needs to be linked to the various notions of sustainability, acknowledging a hierarchy of considerations underlying decision-making on trade-offs, thus allowing political and moral arguments to play a proper role in the strategy towards sustainable intensification. We make a plea to create clarity in assumptions, norms and values in that decision-making process. Acknowledging that win-win situations are rare and that (some) choices have to be made on non-scientific grounds makes the debate more transparent and its outcome more acceptable both to the scientific community and society at large.