That scientific modelling should aim to take into account uncertainty, is by now widely accepted. Most scholars use probabilities to describe this uncertainty. This project, on the other hand, is concerned with imprecise probabilities. Simply put, in its most basic form, an imprecise probability model is a set of probability models, each of which is a candidate for some ideal true but unknown probability model. These imprecise models are typically useful whenever sharp, precise and trustworthy assessments of probabilities are not available, for example because it is too difficult, costly, or time-consuming to gather sufficient data or expert knowledge. In such cases, standard probability models, and the inferences and decisions that are derived from them, are often unreliable. Imprecise probability models avoid this problem by allowing for partial probability assessments such as bounds on probabilities. The resulting inferences and decisions are robust with respect to variations within these bounds, and as such remain reliable even in case of severe uncertainty. These benefits come at the cost of having to deal with more involved models with lesser known properties though. The aim of this project is to further develop the field of imprecise probabilities, so as to overcome these challenges.