To improve the census of the Upper Sco association (~11 Myr, ~145 pc), we have identified candidate members using parallaxes, proper motions, and color-magnitude diagrams from several wide-field imaging surveys and have obtained optical and infrared spectra of several hundred candidates to measure their spectral types and assess their membership. We also have performed spectroscopy on a smaller sample of previously known or suspected members to refine their spectral types and evidence of membership. We have classified 530 targets as members of Upper Sco, 377 of which lack previous spectroscopy. Our new compilation of all known members of the association contains 1631 objects. Although the census of Upper Sco has expanded significantly over the last decade, there remain hundreds of candidates that lack spectroscopy. The precise parallaxes and proper motions from the second data release of Gaia should extend down to substellar masses in Upper Sco, which will greatly facilitate the identification of the undiscovered members.