We have performed a survey for new members of the Ophiuchus cloud complex using high-precision astrometry from the second data release of Gaia, proper motions measured with multi-epoch images from the Spitzer Space Telescope, and color-magnitude diagrams constructed with photometry from various sources. Through spectroscopy of candidates selected with those data, we have identified 155 new young stars. Based on available measurements of kinematics, we classify 102, 47, and six of those stars as members of Ophiuchus, Upper Sco, and other populations in Sco-Cen, respectively. We have also assessed the membership of all other stars in the vicinity of Ophiuchus that have spectroscopic evidence of youth from previous studies, arriving at a catalog of 373 adopted members of the cloud complex. For those adopted members, we have compiled mid-IR photometry from Spitzer and the Wide-field Infrared Survey Explorer and have used mid-IR colors to identify and classify circumstellar disks. We find that 210 of the members show evidence of disks, including 48 disks that are in advanced stages of evolution. Finally, we have estimated the relative median ages of the populations near the Ophiuchus clouds and the surrounding Upper Sco association using absolute K-band magnitudes (M K ) based on Gaia parallaxes. If we adopt an age 10 Myr for Upper Sco, then the relative values of M K imply median ages of ~ 2 Myr for L1689 and embedded stars in L1688, 3-4 Myr for low-extinction stars near L1688, and ~ 6 Myr for the group containing ρ Oph.