Player behavioural modelling has grown from a means to improve the playing strength of computer programs that play classic games (e.g., chess), to a means for impacting the player experience and satisfaction in video games, as well as in cross-domain applications such as interactive storytelling. In this context, player behavioural modelling is concerned with two goals, namely (1) providing an interesting or effective game AI on the basis of player models and (2) creating a basis for game developers to personalise gameplay as a whole, and creating new user-driven game mechanics. In this article, we provide an overview of player behavioural modelling for video games by detailing four distinct approaches, namely (1) modelling player actions, (2) modelling player tactics, (3) modelling player strategies, and (4) player profiling. We conclude the article with an analysis on the applicability of the approaches for the domain of video games.