In the presence of strong external fields and steep gradients the flux formulae are not linear. The relation between the flux and the diffusion coefficient must be modified. The different flux-limited theories are presented. The flux formulae for solid systems far from equilibrium are derived and different forms of phenomenological flux limiters are discussed. It is shown that in order to accurately compute diffusion flow that is generated by strong force fields and/or discontinuities, the flux-limited diffusion must be considered. The flux limiters improve the spatial accuracy and allow to avoid baseless oscillations in the solutions.