This paper discusses how epistemic uncertainties are currently considered in the most widely occurring natural hazard areas, including floods, landslides and debris flows, dam safety, droughts, earthquakes, tsunamis, volcanic ash clouds and pyroclastic flows, and wind storms. Our aim is to provide an overview of the types of epistemic uncertainty in the analysis of these natural hazards and to discuss how they have been treated so far to bring out some commonalities and differences. The breadth of our study makes it difficult to go into great detail on each aspect covered here; hence the focus lies on providing an overview and on citing key literature. We find that in current probabilistic approaches to the problem, uncertainties are all too often treated as if, at some fundamental level, they are aleatory in nature. This can be a tempting choice when knowledge of more complex structures is difficult to determine but not acknowledging the epistemic nature of many sources of uncertainty will compromise any risk analysis. We do not imply that probabilistic uncertainty estimation necessarily ignores the epistemic nature of uncertainties in natural hazards; expert elicitation for example can be set within a probabilistic framework to do just that. However, we suggest that the use of simple aleatory distributional models, common in current practice, will underestimate the potential variability in assessing hazards, consequences, and risks. A commonality across all approaches is that every analysis is necessarily conditional on the assumptions made about the nature of the sources of epistemic uncertainty. It is therefore important to record the assumptions made and to evaluate their impact on the uncertainty estimate. Additional guidelines for good practice based on this review are suggested in the companion paper (Part 2).