Upon the choice of an Eulerian observer adapted to a 3 + 1 spacetime foliation and suitable fluid and magnetic field variables, it is possible to cast the equations of both general relativistic (inviscid) hydrodynamics (GRHD) and (ideal) magneto-hydrodynamics (GRMHD) as first-order, hyperbolic systems of conservation laws for state-vectors comprising the densities of mass, momentum, energy and magnetic field components. Hyperbolicity allows the use of the flux-vector Jacobians wave structure to build up stable and accurate numerical schemes for their solution. In recent years, the so-called Godunov-type schemes, based upon approximate Riemann solvers, have been successfully extended from classical to relativistic fluid dynamics (both special and general). While such advances also hold true in the case of the MHD equations, the development still awaits here for a thorough numerical exploration. This paper reports formulations of the GRHD/GRMHD equations amenable to numerical investigations using Godunov-type schemes. A number of relevant applications in the field of relativistic astrophysics is also covered.