The Benamou-Brenier dynamical formulation of optimal transport has had a tremendous impact on both the theoretical and applied aspects of the theory. In contrast, no such dynamical formulation existed for multi-marginal optimal transport. Together with Brendan Pass we developed a theory of dynamical multi-marginal optimal transport, which provides new results even in the classical two-marginal case. In this talk I will explain our dynamical formulation and how it can be solved numerically.