This paper presents a spectroscopic redshift survey of 73 submillimeter (submm) galaxies (SMGs) using the Keck-I telescope. The galaxies, with a median 850 μm flux density of 5.7 mJy, span redshifts from 1.7 to 3.6, with a median redshift of 2.2. The authors model the selection function of their radio-identified sample and find that the median redshift is 2.3, similar to that of optically- and radio-selected quasars. The observed redshift distributions are consistent for both active galactic nuclei (AGN) and starburst sub-samples. The median $R_{AB}$ magnitude is 24.6, but the dust-corrected ultraviolet (UV) luminosities of the galaxies are significantly lower than expected from their radio/submm emission, underestimating their true luminosities by a median factor of $\sim 100$. Radio and submm observations are crucial for selecting the most luminous, high-redshift galaxies. The authors estimate dust temperatures and characterize photometric redshifts using 450 μm measurements, confirming that the median dust temperature of $T_d = 36 \pm 7$ K is reasonable. They calculate total infrared and bolometric luminosities, construct a luminosity function, and quantify the evolution of the submm population across $z = 0.5$–3.5. The authors determine a lower limit to the AGN content of the population and measure the contribution of highly-obscured, luminous galaxies to the luminosity density history of the Universe. They conclude that bright submm galaxies contribute a comparable star formation density to Lyman-break galaxies at $z = 2$–3 and may be the dominant site of massive star formation at this epoch. The rapid evolution of submm galaxies and QSO populations contrasts with that seen in bolometrically lower luminosity galaxy samples, suggesting a close link between submm galaxies and the formation and evolution of galactic halos hosting QSOs.This paper presents a spectroscopic redshift survey of 73 submillimeter (submm) galaxies (SMGs) using the Keck-I telescope. The galaxies, with a median 850 μm flux density of 5.7 mJy, span redshifts from 1.7 to 3.6, with a median redshift of 2.2. The authors model the selection function of their radio-identified sample and find that the median redshift is 2.3, similar to that of optically- and radio-selected quasars. The observed redshift distributions are consistent for both active galactic nuclei (AGN) and starburst sub-samples. The median $R_{AB}$ magnitude is 24.6, but the dust-corrected ultraviolet (UV) luminosities of the galaxies are significantly lower than expected from their radio/submm emission, underestimating their true luminosities by a median factor of $\sim 100$. Radio and submm observations are crucial for selecting the most luminous, high-redshift galaxies. The authors estimate dust temperatures and characterize photometric redshifts using 450 μm measurements, confirming that the median dust temperature of $T_d = 36 \pm 7$ K is reasonable. They calculate total infrared and bolometric luminosities, construct a luminosity function, and quantify the evolution of the submm population across $z = 0.5$–3.5. The authors determine a lower limit to the AGN content of the population and measure the contribution of highly-obscured, luminous galaxies to the luminosity density history of the Universe. They conclude that bright submm galaxies contribute a comparable star formation density to Lyman-break galaxies at $z = 2$–3 and may be the dominant site of massive star formation at this epoch. The rapid evolution of submm galaxies and QSO populations contrasts with that seen in bolometrically lower luminosity galaxy samples, suggesting a close link between submm galaxies and the formation and evolution of galactic halos hosting QSOs.