Choice models have been applied to explain and predict the transportation choices of individuals for half a century. The advent of big data brings about new opportunities and poses new challenges for forecasting. This chapter discusses the major methodological contributions and the most recent developments in the field of choice modelling in transportation. Advanced choice models have been proposed to accommodate unrestricted substitution patterns between alternatives, unobserved taste variations, serial correlation between repeated observations, and latent constructs as attitudes and perceptions. In recent years, data-driven methods have gained traction to improve the prediction accuracy and to assist the analyst in the model specification. Choice models have also been incorporated into optimization problems to account for the interactions between the choices of individuals and the planning decisions under evaluation. To estimate these advanced models, fast and computationally efficient methods are required.