Gamma-ray bursts (GRBs) are the brightest explosions in the universe. During its roughly 20 second duration, a single burst outshines a supernova (in light) by a factor of about 10 billion. Since 1998, observations have linked the most abundant class of GRBs - the "long soft" variety - with supernovae of an unusual variety, and it is now thought that all GRBs of this class are accompanied by simultaneous supernovae (though less than 1 per cent of supernovae are GRBs). One of the leading models for GRBs is the collapse of the iron core of a massive star to a black hole and an accretion disk - the so called "collapsar model". Using a special relativistic, adaptive mesh code, we are exploring, in 2D and 3D, the collapse of the rotating star to a hole and disk, the formation of relativistic polar outflows, and the propagation of the resulting jet through the star. From these SciDAC-sponsored calculations, we are learning the conditions where relativistic jets might form and how a jet of given characteristics interacts with the star to produce diverse observational phenomena. In a parallel study, we are trying to understand just what makes a massive star choose to be a GRB rather than an ordinary supernova. The most likely answer is rotation. If so, one might expect a continuum of events between relativistic polar explosions (GRBs) and mildly deformed, slower moving explosions (supernovae).