Abstract: This talk presents a brief overview of numerical relativity simulations of two scenarios of relativistic astrophysics which are among the most important sources of gravitational radiation. I will start discussing binary neutron star mergers and the evolution of the resulting black hole–torus systems, and will then continue to discuss the gravitational collapse of rotating stars massive enough to produce similar types of black hole-torus systems. Either scenario has features compatible with the events producing short–hard and long-soft gamma-ray bursts, respectively. The underlying numerical work is based on a basic theoretical framework which comprises the Einstein equations for the gravitational field and the hydrodynamics equations for the evolution of the matter fields. The most well-established formulations for both systems of equations will be briefly discussed, along with the numerical methods best suited for their numerical solution, namely high-order finite-differencing for the case of the gravitational field equations and high-resolution shock-capturing schemes for the case of the relativistic Euler equations. A number of recent results regarding the dynamics of the events, the possible outcomes, and the gravitational wave emission will be reviewed.