Three billions years after the Big Bang, the rate at which galaxies in the Universe were forming stars was at its peak. Colloquially known as Cosmic Noon, this epoch (redshift z ~ 2) is crucial to our understanding of how galaxies evolve with time. Dusty star-forming galaxies (DSFGs) offer important clues to such fueling and quenching of star formation. With extreme infrared luminosities (1012 − 1014 solar luminosities), their inferred star formation rates are 100−10000 solar masses per year. Yet, the physical mechanisms by which they fuel this short-lived maximal starburst phase remain poorly understood. With this dissertation, I will dissect the structure and motions of gas, dust, and stars in ~30 of the brightest DSFGs ever discovered, which are all gravitationally lensed. To capture their intrinsic properties, we derive parametric lens models to account for the distortion and amplification due to strong lensing. We find that they are only modestly magnified by a factor of ~10, implying that they are among the rare set of objects that exceed 1013 solar luminosities. Despite their scarcity, they appear to be simply the extreme limit of more typical DSFGs. Their dust continuum-emitting regions are larger, suggesting that their unusually-elevated star formation rates are due to more spatially-extended sites of stellar mass assembly. This is contrary to prevailing theories that DSFGs are regulated by a limit in star formation density, beyond which radiation pressure from young stars disrupts the collapse of molecular gas, which is necessary to continue forming stars. Other mechanisms may be responsible for extinguishing their prodigious rates of star formation. For one object, we study the dynamical structure of molecular gas, and find it largely consistent with a massive, rotating disk-like structure, lacking the dominant turbulent motions expected from major galaxy mergers. Finally, I introduce a novel method to efficiently predict magnification factors of lensed objects without the need for intensive lens modeling. As the number of known lensed DSFGs continues to grow, it is imperative that we devise ways to quickly characterize them so that follow-up studies can be targeted towards the most compelling objects.