The various possibilities for the origin ("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. Using high-mass binary stellar population synthesis models, I quantify the expected spatial extent around galaxies of coalescing neutron stars, one of the leading contenders for GRB progenitors. I then test this scenario 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 (and, similarly, blackhole-neutron star coalescences); instead, the distribution is statistically consistent with a population of progenitors that closely traces the ultraviolet light of galaxies. This is naturally explained by bursts which originate from the collapse of massive stars ("collapsars"). This claim is further supported by the unambiguous detections of intermediate-time (approximately three weeks after the bursts) emission "bumps" which appear substantially more red than the afterglows themselves. I claim that these bumps could originate from 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 at least some long-duration GRBs. Regardless of the true physical origin of these bumps, it appears that all viable alternative models of these bumps (such as dust scattering of the afterglow light) require a substantial amount of circumburst matter that is distributed as a wind-stratified medium; this too, implicates massive stars. Also suggested herein are some future observations which could further solidify or refute the supernova claim. In addition to the observational and modeling 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. viii