The association of “long” Gamma-Ray Bursts (durations > 2 seconds) with peculiar Type Ic supernovae suggests strongly that this type of GRB is produced by the collapse of the rapidly rotating core of an initially very massive star to a black hole. At the time of collapse the star has lost its hydrogen-rich envelope and the GRB is thought to be produced by a collimated relativistic jet of matter ejected along the star's rotation axis. The angular momentum constraints for producing such a “collapsar” or “hypernova” suggest that the GRB-producing core collapses constitute only a small fraction of all core collapses of massive stars. As to the short-duration GRBs (< 2 seconds), which make up about one third of all GRBs, the most favoured model is that of the coalescence of a double neutron star or of a neutron star-black hole binary. Also these events are expected to be very rare, having a frequency of at most one event per hundred thousand years for a galaxy like our own. Due to the collimation of the relativistically ejected matter, the observable frequency of GRB events will, like in the case of the “long” bursts, be at least a factor hundred smaller.