The diversity of stellar death is revealed in the energy, velocity and geometry of the explosion debris ("ejecta"). Using multi-wavelength observations of gamma-ray burst (GRB) afterglows I show that GRBs, arising from the death of massive stars, are marked by relativistic, collimated ejecta ("jets") with a wide range of opening angles. I further show that the jet opening angles are strongly correlated with the isotropic-equivalent kinetic energies, such that the true relativistic energy of GRBs is nearly standard, with a value of few times 10^51 erg. A geometry-independent analysis which relies on the simple non-relativistic dynamics of GRBs at late time confirms these inferences. Still, the energy in the highest velocity ejecta, which give rise to the prompt gamma-ray emission, is highly variable. These results suggest that various cosmic explosions are powered by a common energy source, an "engine" (possibly an accreting stellar-mass black hole), with their diverse appearances determined solely by the variable high velocity output.On the other hand, using radio observations I show that local type Ibc core-collapse supernovae generally lack relativistic ejecta and are therefore not powered by engines. Instead, the highest velocity debris in these sources, typically with a velocity lower than 100,000 km/sec, are produced in the (effectively) spherical ejection of the stellar envelope. The relative rates of engine- and collapse-powered explosions suggest that the former account for only a small fraction of the stellar death rate. Motivated by the connection of GRBs to massive stars, and by their ability to overcome the biases inhenert in current galaxy surveys, I investigate the relation between GRB hosts and the underlying population of star-forming galaxies. Using the first radio and submillimeter observations of GRB hosts, I show that some are extreme starburst galaxies with the bursts directly associated with the regions of most intense star formation. I suggest, by comparison to other well-studied samples, that GRBs preferentially occur in sub-luminous, low mass galaxies, undergoing the early stages of a starburst process. If confirmed with future observations, this trend will place GRBs in the forefront of star formation and galaxy evolution studies.