  Numerical schemes for the general relativistic hydrodynamic equations are
discussed. The use of conservative algorithms based upon the characteristic
structure of those equations, developed during the last decade building on
ideas first applied in Newtonian hydrodynamics, provides a robust methodology
to obtain stable and accurate solutions even in the presence of
discontinuities. The knowledge of the wave structure of the above system is
essential in the construction of the so-called linearized Riemann solvers, a
class of numerical schemes specifically designed to solve nonlinear hyperbolic
systems of conservation laws. In the last part of the review some astrophysical
applications of such schemes, using the coupled system of the
  (characteristic) Einstein and hydrodynamic equations, are also briefly
presented.
