I have used high-precision photometry and astrometry from the early installment of the third data release of Gaia (EDR3) to perform a survey for members of the stellar populations within the Sco-Cen complex, which consist of Upper Sco, UCL/LCC, the V1062 Sco group, Ophiuchus, and Lupus. Among Gaia sources with {sigma}{pi}<1mas, I have identified 10509 candidate members of those populations. I have compiled previous measurements of spectral types, Li equivalent widths, and radial velocities for the candidates, which are available for 3169, 1420, and 1740 objects, respectively. In a subset of candidates selected to minimize field star contamination, I estimate that the contamination is <~1% and the completeness is ~90% at spectral types of <~M6-M7 for the populations with low extinction (Upper Sco, V1062 Sco, UCL/LCC). I have used that cleaner sample to characterize the stellar populations in Sco-Cen in terms of their initial mass functions, ages, and space velocities. For instance, all of the populations in Sco-Cen have histograms of spectral types that peak near M4-M5, which indicates that they share similar characteristic masses for their initial mass functions (~0.15-0.2M{sun}). After accounting for incompleteness, I estimate that the Sco-Cen complex contains nearly 10000 members with masses above ~0.01M{sun}. Finally, I also present new estimates for the intrinsic colors of young stars and brown dwarfs (<~20Myr) in bands from Gaia EDR3, the Two Micron All Sky Survey, the Wide-field Infrared Survey Explorer, and the Spitzer Space Telescope.