  This paper reviews different numerical methods for specific examples of
Wasserstein gradient flows: we focus on nonlinear Fokker-Planck equations,but
also discuss discretizations of the parabolic-elliptic Keller-Segel model and
of the fourth order thin film equation. The methods under review are of
Lagrangian nature, that is, the numerical approximations trace the
characteristics of the underlying transport equation rather than solving the
evolution equation for the mass density directly. The two main approaches are
based on integrating the equation for the Lagrangian maps on the one hand, and
on solution of coupled ODEs for individual mass particles on the other hand.
