Gravitational waves, which are predicted by Einstein's theory of
General Relativity, are potentially emitted by various astrophysical sources like black holes, neutron stars or collapsing stellar cores. Several extremely sensitive detectors have recently started to search for these waves, and confirmed detections could open a new window on the Universe in the near future. In parallel to the experimental efforts, in the first decade of the new millennium new numerical and mathematical approaches in combination with powerful computers have paved the way to accurately modeling the astrophysical sources and the expected waveforms. I will present those advances, with particular focus on the supernova core collapse scenario, which is a very rich and challenging physical phenomenon. I will also propose directions for future research in source modeling, aiming at realistic computer simulations of the collapsar model that could explain the enigmatic cosmic gamma-ray bursts and making use of massively parallel supercomputers.