Recently, several authors have presented interesting contributions on how to meet deep or severe uncertainties in a risk analysis setting. In this article, we provide some reflections on some of the foundational pillars that this work is based on, including the meaning of concepts such as deep uncertainty, known probabilities, and correct models, the aim being to contribute to a strengthening of the scientific platform of the work, as well as providing new insights on how to best implement management policies meeting these uncertainties. We also provide perspectives on the boundaries and limitations of analytical approaches for supporting decision making in cases of deep uncertainties. A main conclusion of the article is that deep uncertainties call for managerial review and judgment that sees beyond the analytical frameworks studied in risk assessment and risk management contexts, including those now often suggested to be used, such as robust optimization techniques. This managerial review and judgment should be seen as a basic element of the risk management.