Abstract: Dusty star-forming galaxies (DSFGs) represent an extreme phase of rapid dust-obscured galaxy assembly and are major contributors to the cosmic star-formation rate density (SFRD) at early times. For some time, a comprehensive understanding of the formation and evolution of DSFGs has been hindered by the difficulty of reliably identifying large, deep samples and determining their redshifts and physical properties. In my thesis, I present several studies using Atacama Large Millimeter/submillimeter Array (ALMA) and James Webb Space Telescope (JWST) observations to characterize the DSFG population, with a particular emphasis on the faint submillimeter population. First, I use multi-band ALMA observations of 870 μm-selected DSFGs to model their dust spectral energy distributions (SEDs) to high precision, showing that the dust properties of sources at cosmic noon are generally consistent with those seen in local galaxies and predicted by models. Using follow-up ALMA linescans along with ancillary JWST and ground-based redshifts for this sample, I construct a nearly (97%) complete spectroscopic redshift distribution for S850μm > 2 mJy DSFGs for the first time. The results illustrate the effectiveness of combining ALMA and JWST to measure DSFG redshifts, and they demonstrate that JWST is particularly effective at obtaining even high redshifts for DSFGs. However, the JWST coverage is just ~30% in the best-covered fields. I use these redshifts to test photometric redshift estimation methods and to constrain the shape of the DSFG redshift distribution. Next, I use ALMA 1.2 mm data to verify that a JWST NIR-color selection can determine accurate positions for single-dish submillimeter (JCMT/SCUBA-2) sources, including faint (S850μm < 2 mJy) DSFGs. Using panchromatic SED fits and surface brightness profile fitting, I measure the physical properties and morphologies of these NIR-selected DSFGs, finding that they sit in a lower star-formation rate (SFR) regime (SFR ~ 50-150 Msun/yr) than that probed by typical single-dish 850 μm surveys. The stellar masses and morphologies of the bright (S850μm > 2 mJy) sources are remarkably similar to those of the faint sources. Finally, I observe a low fraction of major mergers in constrast with previous studies based on rest-frame optical wavelengths, suggesting that these studies were impacted by severe dust attenuation. By helping to infer the properties of larger samples detected in future wide surveys, these studies will contribute to a precise mapping of the dust-obscured SFRD and structure assembly history of the Universe.