This communication is an introduction to recent methods for the numerical simulation of non-Newtonian viscoplastic and viscoelastic fluid flows. For both viscoelastic and viscoplastic problems, practical computations and recent error estimates results are presented in the framework of the mixed finite elements method. In the first part of the presentation, new algorithms for the numerical approximation of viscoelastic fluid with a differential constitutive equation are considered. In a second part, some recent auto-adaptive mesh methods for the resolution of viscoplastic problems are developed. The third part of the presentation is an introduction to the Rheolef library, a free software solution for the resolution of such problems with the finite elements method.