This paper presents a survey of 73 submillimeter (submm) galaxies (SMGs) with spectroscopic redshifts, obtained using the Keck-I telescope. The sample includes galaxies with a median 850 μm flux density of 5.7 mJy, detected through their faint radio emission. The galaxies are found at redshifts up to z = 3.6, with a median redshift of 2.2. Modeling a purely submm flux-limited sample suggests a median redshift of 2.3, with a redshift distribution similar to optically- and radio-selected quasars. The redshift distributions are similar for AGN and starburst sub-samples. The median R_AB magnitude is 24.6, but dust-corrected ultraviolet (UV) luminosities are much lower than the bolometric luminosities inferred from radio/submm emission, underestimating the true luminosity by a median factor of ~100 for SMGs with pure starburst spectra. Radio and submm observations are essential for selecting the most luminous, high-redshift galaxies. The 850 μm, radio, and redshift data are used to estimate dust temperatures and characterize photometric redshifts. Using 450 μm measurements, the median dust temperature is found to be 36 ± 7 K, consistent with the local FIR–radio correlation at high redshift. Individual 450 μm detections are consistent with the local radio-FarIR relation at z ~ 2. The median dust temperature is lower than that estimated for similarly luminous IRAS 60 μm galaxies locally. Dust temperature variations make it impossible to estimate redshifts for individual submm galaxies using simple long-wavelength photometric methods to better than Δz ≈ 1. Total infrared and bolometric luminosities are calculated, and a luminosity function is constructed. The submm population shows strong evolution across z = 0.5–3.5 relative to local IRAS galaxies. The bolometric luminosities and UV-spectral classifications are used to determine a lower limit to the active galactic nucleus (AGN) content of the population. The study concludes that bright submm galaxies contribute a comparable star formation density to Lyman-break galaxies at z = 2–3, and that this population 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 selected in the restframe UV, suggesting a close link between submm galaxies and the formation and evolution of the galactic halos which host QSOs.This paper presents a survey of 73 submillimeter (submm) galaxies (SMGs) with spectroscopic redshifts, obtained using the Keck-I telescope. The sample includes galaxies with a median 850 μm flux density of 5.7 mJy, detected through their faint radio emission. The galaxies are found at redshifts up to z = 3.6, with a median redshift of 2.2. Modeling a purely submm flux-limited sample suggests a median redshift of 2.3, with a redshift distribution similar to optically- and radio-selected quasars. The redshift distributions are similar for AGN and starburst sub-samples. The median R_AB magnitude is 24.6, but dust-corrected ultraviolet (UV) luminosities are much lower than the bolometric luminosities inferred from radio/submm emission, underestimating the true luminosity by a median factor of ~100 for SMGs with pure starburst spectra. Radio and submm observations are essential for selecting the most luminous, high-redshift galaxies. The 850 μm, radio, and redshift data are used to estimate dust temperatures and characterize photometric redshifts. Using 450 μm measurements, the median dust temperature is found to be 36 ± 7 K, consistent with the local FIR–radio correlation at high redshift. Individual 450 μm detections are consistent with the local radio-FarIR relation at z ~ 2. The median dust temperature is lower than that estimated for similarly luminous IRAS 60 μm galaxies locally. Dust temperature variations make it impossible to estimate redshifts for individual submm galaxies using simple long-wavelength photometric methods to better than Δz ≈ 1. Total infrared and bolometric luminosities are calculated, and a luminosity function is constructed. The submm population shows strong evolution across z = 0.5–3.5 relative to local IRAS galaxies. The bolometric luminosities and UV-spectral classifications are used to determine a lower limit to the active galactic nucleus (AGN) content of the population. The study concludes that bright submm galaxies contribute a comparable star formation density to Lyman-break galaxies at z = 2–3, and that this population 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 selected in the restframe UV, suggesting a close link between submm galaxies and the formation and evolution of the galactic halos which host QSOs.