AbstractEmission line profiles from pre-main-sequence objects accreting via magnetically-controlled funnel flows encode information on the geometry and kinematics of the material on stellar radius scales. In order to extract this information it is necessary to perform radiative-transfer modelling of the gas to produce synthetic line profiles. In this review I discuss the physics that needs to be included in such models, and the numerical methods and assumptions that are used to render the problem tractable. I review the progress made in the field over the last decade, and summarize the main successes and failures of the modelling work.