The various possibilities for the progenitors of gamma-ray bursts (GRBs) manifest in differing observable properties. Through deep spectroscopic and high-resolution imaging observations of some GRB hosts, I demonstrate that well-localized long-duration GRBs are connected with otherwise normal star-forming galaxies at moderate redshifts of order unity. I test various progenitor scenarios by examining the offset distribution of GRBs about their apparent hosts, making extensive use of ground-based optical data from Keck and Palomar and space-based imaging from the Hubble Space Telescope. The offset distribution appears to be inconsistent with the coalescing neutron star binary hypothesis but statistically consistent with a population of progenitors that closely traces the ultra-violet light of galaxies. This is naturally explained by bursts which originate from the collapse of massive stars. This claim is further supported by the unambiguous detections of emission ``bumps’’ which can be explained as supernovae that occur at approximately the same time as the associated GRB; if true, GRB 980326 and GRB 011121 provide strong observational evidence connecting cosmological GRBs to high-redshift supernovae and implicate massive stars as the progenitors of some long-duration GRBs. Interestingly, most alternative models of these bumps require wind-stratified circumburst media; this too, implicates massive stars. In addition to this work, I also constructed the Jacobs Camera (JCAM), a dual-beam optical camera for the Palomar 200-inch Telescope designed to follow-up rapid GRB localizations (abridged).