Epistemicuncertainties appear across all engineering fields to quite some significantextent. Although they can often be described phenomenologically andqualitatively, they counteract a rigorous quantitative description, which isneeded as a basis for a realistic risk assessment. In the presence of epistemicuncertainties the specification of a probabilistic model and the associatedrisk analysis lead to hypothetical results presuming some intuitive guess tocapture the influence of the epistemic uncertainty. That is, we quantify riskbased on conditions that represent assumptions rather than facts. Such resultscan be significantly misleading. It is thus of paramount importance to quantifyepistemic uncertainties most realistically. This quantification should neitherintroduce unwarranted information nor should it neglect information. On thisbasis there is a clear consensus that epistemic uncertainties need to be takeninto account for a realistic assessment of risk and reliability. However, thereis no clearly defined procedure to master this challenge. There are rather avariety of concepts and approaches available to deal with epistemicuncertainties, from which the engineer can chose. This choice is made difficultby the perception that the available concepts are competing and opposed to oneanother rather than being complementary and compatible. Clearly, the firstconsideration should be devoted to a probabilistic modelling, naturally throughsubjective probabilities, which express a belief of the expert and can beintegrated into a fully probabilistic framework in a coherent manner via aBayesian approach. While this pathway is widely accepted and recognized asbeing very powerful, the potential of set-theoretical approaches and impreciseprobabilities has only been utilized to some minor extent. Those approaches,however, attract increasing attention in cases when available information isnot rich enough to meaningfully specify subjective probability distributions.The presentation will feature models for epistemic uncertainties, and it willhighlight their capabilities and added value when used for engineering analysisand design. Illustrative examples are used to explain the respective features.The discussion on the models is complemented by presenting a powerful numericaltechnology for processing epistemic uncertainties even in very complex andnonlinear engineering analyses. This technology can be used not only forreliability analysis, but also for sensitivity analysis, design, model updatingand more.