This is a dissertation in six chapters, where we aim to obtain a better understanding of the most luminous source populations at the peak epoch of cosmic star formation rate density using observational data collected with state-of-the-art facilities. Previous studies report star formation rates (SFR) comparable to and even exceeding the local ultra-luminous IR galaxy (ULIRG) for a population of dust-obscured (IR)-luminous starbursting galaxies discovered at z>2 (dubbed dusty star-forming galaxies, DSFG), but the ULIRGs and DSFGs have different global star formation and interstellar medium (ISM) properties. Meanwhile, a picture connecting the evolution of dust-obscured starburst galaxies and the growth of supermassive black holes (SMBHs) has emerged under the “quasar-starburst co-evolutionary link” paradigm. This body of work examines the nature and origin of the most extreme DSFGs and the postulated quasar-starburst co-evolution picture by examining the ISM conditions, gas kinematics and morphologies of these high-z galaxy populations using a suite of radio/sub-millimeter interferometers (e.g., ALMA, the VLA, NOEMA), complemented by data taken with space-based facilities such as SOFIA and the HST. Leveraging multi-wavelength photometry and (sub-)kpc resolution imaging of CO and far-infrared (FIR)-bright lines (e.g.,[CII]) enabled by the latest instrument and facilities, we examine how the morphology of DSFG varies with molecular gas fractions and IR luminosities, and how the molecular gas fraction, IR luminosity, and active galactic nucleus (AGN) luminosity are related, as postulated in the quasar-starburst evolutionary picture; and study properties of the gas, stellar, and dust components of high-z DSFG and quasar host galaxies. In the detailed case studies of high-z quasars, we find that the decreased in molecular gas fraction at intermediate redshift (0 <z<1) compared to the peak epoch of star formation and BH accretion may be the main driver in the decline in the cosmic star formation history (SFH) and BH accretion rate density; we do not find evidence of AGN feedback on the molecular gas fraction in the intermediate redshift quasar RXJ1131; and that the SMBH in intermediate redshift quasars like RXJ1131 appear to have assembled its BH mass earlier than its stellar bulge. For quasars at z>2, we find that a DSFG hosting a type-2 AGN shows molecular ISM properties consistent with being a hybrid source in the quasar-starburst evolutionary sequence. We also find that the AGN-corrected SFR of one of the most frequently studied high-z quasar (APM 08279+5255) is underestimated in previous work, and that high-z quasars likely have different dust distributions and compositions compared to nearby Seyfert galaxies. In the detailed case study of one of the most luminous DSFG at z∼3, we find direct evidence of disk-wide star formation and evidence suggesting its close resemblance to the local LIRG Arp 220. We also provide the first spatially resolved [CII] imaging at such redshift to examine the physics behind the L[CII]/LFIR −FIR surface density relation and the so-called "[CII]-deficit" problem.