  Recent years have seen a significant progress in the development of general
relativistic codes for the numerical solution of the equations of
magnetohydrodynamics in spacetimes with high and dynamical curvature. These
codes are valuable tools to explore the large-scale plasma dynamics such as
that takes place when two neutron stars collide or when matter accretes onto a
supermassive black hole. This chapter is meant to provide a very brief but
complete overview of the set of equations that are normally solved in modern
numerical codes after they are cast into a conservative formulation within a
3+1 split of spacetime.
