We describe the results of two separate studies of the influence of shape and cohesion on the rheophysics of granular materials, both based on discrete numerical simulations. The fist one compares dense flows of dry frictional spheres and polyhedra down a rough inclined plane. The flow diagrams and constitutive laws previously established for spheres are extended to polyhedra : in both cases, solid fraction and effective friction variations with inertial number can be described as linear over a certain range. In the case of polyhedra, there is a significant increase of the effective friction, while the wall roughness tends to jam the flow in a bottom layer, a few diameters thick. The second study investigates steady - state, pressure - controlled simple shear flows of frictional cohesive disks or spheres. Interparticle cohesion may result from van der Waals or capillary forces, and introduces a dimensionless cohesion number comparing confining forces to contact tensile strength. It is shown that the rheophysics is well described by simple dependencies of solid fraction and effective friction on both inertial and cohesion numbers. Moreover, both studies provide microstructural insight on the origin of the constitutive laws : role of face-to-face contacts in polyhedral assemblies, characterisation of density inhomogeneities and sensitivity to attractive force range in cohesive flow.