We consider a model describing suspensions of rod-like molecules in a solvent fluid. The model consists of a kinetic equation modeling the evolution of a microstructure coupled to a macroscopic Navier-Stokes or Stokes flow through a moment equation for the viscoelastic stress. One objective is to compare such models with traditional models used in macoscopic viscoelasticity like the well known Oldroyd model. We provide a quantitative analysis of cluster formation. We discuss the instability of the quiescent flow and the derivation of the collective response in the diffusive regime. We derive a reduced model for the description of the collective flow that ammounts to a flux-limited Keller-Segel model, and show that it describes well the aggregate response of the sedimenting suspension. (joint with Ch. Helzel)