  Tumour invasion is an essential stage of cancer progression. Its main drivers
are diffusion and taxis, a directed movement along the gradient of a stimulus.
Here we review models with flux limited diffusion and/or taxis which have
applications in modelling of cell migration, particularly in cancer. Flux
limitation ensures control upon propagation speeds, precluding unnaturally
quick spread which is typical for traditional parabolic equations. We recall
the main properties of models with flux limitation effects and discuss ways to
construct them, concentrating on multiscale derivations from kinetic transport
equations.
