The theory of nonlinear evolution equations of diffusive type contains paradigmatic examples that have been studied and are studied at this moment, like the porous medium equation and the p-laplacian equation. In recent times anisotropic flows have attracted attention. We show how to deal with anisotropy in the above mentioned cases and obtain the existence of a nonlinear semigroup with good properties, the construction of the related anisotropic selfsimilar solutions and proof of asymptotic convergence. Many open problems can be discussed. This is work with F. Feo and B. Volzone from Naples.