Normally the transport observed in tokamak experiments greatly exceeds that of collisional transport theory and this anomalous transport is usually attributed to turbulent fluctuations arising from various micro-instabilities, eg drift waves or pressure gradient driven ballooning modes. However, no theoretical model has yet been proposed which adequately describes all of the many fascinating features tokamak transport displays. In this paper the experimental observations that a transport model would need to satisfy are reviewed. Then the theoretical concepts m d tools available for constructing models are outlined. The principal models that have emerged from these considerations are described and the results of detailed comparisons with ,a number of experiments around the world are discussed. Finally the present situation regarding transport modelling is summarised.1 Introduction TE, the energy confinement time, as a multiple H of the ITER-89-P scaling law, the condition for ignition in a machine of given size and geometry becomes(') H > F(fx., is, CYT, an) where fx. is the helium ash fraction, fz the impurity fraction and CY= and 01, characterise the temperature and density profiles: eg T = To(l -T ~/ ~* ) ~T .The prospects for ignition in ITER can be assessed by using reasonable values for the parameters fx.,fZ, CXT and a, (eg lo%, 2% Be, 0.5, 0.25 respectively) and then asking whether experimental confinement modes exist for which H is sufficiently large, say X > 2. Although this approach is reasonably robust it would be far more satisfactory to have a local transport model for energy and particles, including impurities, which would allow calculations of f~., fz, O ~T , 01, and H for given energy and particle sources and boundary conditions at the plasma edge. Furthermore, understanding transport would allow one to seek optimised designs, eg the choice of plasma shape or aspect ratio, and operating scenarios, eg control of current profiles. Finally one could calculate whether the resulting plasma profiles remain stable, eg to MHD instabilities such'as sawteeth, tearing modes and pressure gradient driven instabilities.As well as providing these practical benefits, establishing a local transport model 01995 UEL4EA Fusion