Transformative sustainability science is taking shape in the context of grave difficulties experienced by conventional science. The insights that define this new practice may help us to understand these challenges and find a way to their resolution. The challenges to mainstream science are both external in a loss of public trust and internal in a loss of quality control. They derive ultimately from the changed social situation of science. “Industrialisation” has brought changes in the size of projects, scale of enterprise, and connections with industry. Transformative sustainability science involves a new awareness of scientific argument and of the scientific enquirer. This is best described by four attributes, which function as heuristics. These are complexity; contingency and situatedness; contradiction; and uncertainty and ignorance. In addition there are two “surprise checklists”, applying to images and to devices. These heuristics serve to organise experience and cultivate awareness. They arose out of reflection in teaching and research in transformative sustainability science at the University of Luxembourg in recent years. Their usefulness is attested by the success of that work.