*Abstract:* Geometric numerical integration refers to numerical methods for ordinary and partial differential equations that conserve geometric structure under discretization. For example, an integral preserving numerical time integrators ensures that the numerical solution lives on the intersection of level sets of the first integrals of an ODE, a Lie group integrator preserves an underlying Lie group structure, and a symplectic integrator ensures that the numerical mapping from one time step to the next of a Hamiltonian system is a symplectic map. Generalizations of symplectic integrators have also been introduced for Hamiltonian PDEs, including â€śmultisymplectic integrators". Inviscid fluids have a well known Hamiltonian structure, which has long resisted a satisfying discrete treatment. I will review old work on this, as well as mention some new ideas and near successes...