One of the most exciting broader applications of the study of gamma-ray bursts is in better understanding the star-formation history of the Universe, especially at the highest redshifts. Long-duration GRBs are produced exclusively by massive, young stars, and can be detected beyond z>6 (and potentially even z>9) with small telescopes, pinpointing a SFR-selected sample of galaxies at each redshift unimpeded (in principle) by issues of gas and dust attenuation and without regard to host luminosity. On the other hand, a GRB-selected sample may introduce new biases (such as a dependence on metallicity) that may be difficult to control for, and achieving the goal of an unbiased host-galaxy sample is much more complicated in practice---in particular with regard to the effects of dust attenuation, which can prevent accurate localization of the host. I will discuss recent efforts to shine light upon the population of heavily dust-obscured GRBs and their host galaxies via an ongoing, multi-wavelength campaign with Keck, HST, Spitzer, and the VLA. I will present results showing how a full accounting of these events will influence our view of the relation between the GRB and star-formation rates in the high-redshift universe, as well as conclusions involving the spatial distribution of dust within star-forming galaxies and the efficacy of common assumptions used to estimate star-formation rates in populations of faint galaxies.