An overview of new developments underlying the theoretical framework for filtration of suspensions in viscoelastic media is presented. The linearized capillary hybrid model for viscoelastic flow in porous media is utilized in the extension of the equations for filtration in non-Newtonian media to viscoelastic fluids exhibiting enhanced primary normal stresses in elongational flows. An evaluation of the energy dissipation and a formulation of the friction factor-Reynolds number relationship in conjunction with an additional dimensionless group, N(I) or N(II), for viscoelastic flow in porous media is also presented. The analysis of cake filtration in viscoelastic media has been applied to constant pressure filtration of calcium carbonate slurries in dilute aqueous polyacrylamide solutions.