The area of discrete choice modelling has, over recent years, witnessed the development of ever more flexible model structures that allow for an increasingly realistic representation of travel behaviour. With these developments have also come important issues of specification, estimation and interpretation, some of which are addressed in this thesis, mainly in the context of models allowing for random taste heterogeneity across respondents. As such, it is shown that severe risks of misinterpretation arise when relying on the commonly used Normal distribution, and the advantages of several alternative distributions are illustrated, while also discussing the benefits of a discrete mixture approach. The thesis also highlights risks of confounding between different components of the error structure, and discusses the development of approaches that can lead to computational savings in simulation-based model estimation and application. Finally, a framework is developed for the representation of random variations in a model’s covariance structure. With the pace of theoretical developments, the gap between theory and practice in the use of discrete choice models has widened. The applied part of the thesis aims to partly bridge this gap in one area of travel-behaviour research, looking at the modelling of choices made by air-passengers departing from multi-airport regions, with applications to Greater London and the San Francisco Bay area. The case-studies show the benefits of using advanced model approaches, in this case cross-nesting and random coefficients structures. At the same time however, the work shows that the appeal of such models in largescale analyses is reduced by heightened data requirements, and the significant rise in estimation cost. Finally, the case-studies show that, while the issues discussed in the theoretical part of the thesis need to be taken into account in interpretation, for practical purposes, the guidelines in terms of specification often need to be violated.