This paper presents a review of research on turbine rim sealing with emphasis placed on the underlying flow physics and modelling capability. Rim seal flows play a crucial role in controlling engine disc temperatures but represent a loss from the main engine power cycle and are associated with spoiling losses in the turbine. Elementary models that rely on empirical validation and are currently used in design do not account for some of the known flow mechanisms, and prediction of sealing performance with computational fluid dynamics (CFD) has proved challenging. CFD and experimental studies have indicated important unsteady flow effects that explain some of the differences identified in comparing predicted and measure sealing effectiveness. This review reveals some consistency of investigations across a range of configurations, with inertial waves in the rotating flow apparently interacting with other flow mechanisms which include vane, blade and seal flow interactions, disc pumping and cavity flows, shear layer and other instabilities, and turbulent mixing.