This lecture will provide an overview of past and present work on the mathematical and computational modelling of flow in collapsible tubes. The talk will mainly focus on work done within the biomechanics community. After an overview of a number of physiological applications, the talk will present a review of relevant experimental results. This will be followed by a discussion of a number of mathematical models which have been proposed and analysed over the past decades. Proceeding from 1D to 3D models, the talk will illustrate the main assumptions behind each model and discuss their respective strengths and weaknesses. Finally, an attempt will be made to outline a number of open questions which should be addressed in future work.