Most stars are found in binary or multiple stellar systems. A rare species of of binary systems contains two neutron stars. To date, several of these exotic systems are known, and one of them, the binary pulsar PSR 1913+16, has been studied in detail for almost three decades with an enormous precision. These observations show that the binary orbit is decaying in excellent agreement with the predictions from general relativity making the final merger of the two neutron stars an inescapable consequence. This merger event is for several reasons an extremely interesting topic. Several ground-based gravitational wave detectors are expected to be in operation very soon and neutron star binaries are among the most promising detectable sources. In addition, the coalescence of two neutron stars in a binary system has long been identified as a potential site for a class of cosmological explosions, the so-called gamma-ray bursts. Further interest in this scenario comes from its possible role for the formation of a large fraction of the heaviest elements, that form via rapid neutron capture. These elements have to be formed in an explosion in a neutron-rich environment, exactly the conditions that are encountered in a neutron star merger. I will present results of my latest high-resolution simulations of this event and discuss its observable consequences.