Handling uncertainty in the current European Union (EU) risk assessment of new and existing substances is problematic for several reasons. The known or quantifiable sources of uncertainty are mainly considered. Uncertainty is insufficiently, explicitly communicated to risk managers and decision makers but hidden and concealed in risk quotient numbers that appear to be certain and, therefore, create a false sense of certainty and protectiveness. The new EU chemical policy legislation, REACH, is an opportunity to learn from interdisciplinary thinking in order to evolve to smart risk assessment: an assessment in which awareness and openness to uncertainty is used to produce better characterizations and evaluations of risks. In a smart risk assessment context, quantifying uncertainty is not an aim but just a productive means to refine the assessment or to find alternative solutions for the problem at stake. Guidance and examples are given on how to differentiate, assess, and use uncertainty.