A classical kinematical model of sedimentation of small equal-sized particles dispersed in a viscous fluid leads to a scalar conservation law with a nonlinear flux. Several extensions of this model are reviewed, with a strong focus on recently developed numerical methods. These extensions include a one-dimensional clarifier-thickener model giving rise to a conservation law with discontinuous flux, a conservation law with nonlocal flux, systems of nonlinear conservation modelling the sedimentation of polydisperse suspensions, and
