Pedestrian dynamics is concerned with understanding the movement patterns that arise in places where more than one person walks. Relating theoretical models to data is a crucial goal of research in this field. Statistical model fitting and model selection are a suitable approach to this problem and here we review the concepts and literature related to this methodology in the context of pedestrian dynamics. The central tenet of statistical modelling is to describe the relationship between different variables by using probability distributions. Rather than providing a critique of existing methodology or a "how to" guide for such an established research technique, our review aims to highlight broad concepts, different uses, best practices, challenges and opportunities with a focussed view on theoretical models for pedestrian behaviour. This contribution is aimed at researchers in pedestrian dynamics who want to carefully analyse data, relate a theoretical model to data, or compare the relative quality of several theoretical models. The survey of the literature we present provides many methodological starting points and we suggest that the particular challenges to statistical modelling in pedestrian dynamics make this an inherently interesting field of research.