The high-precision astrometry from the second data release of the Gaia mission (Cat. I/345) has made it possible to greatly improve the census of members of nearby clusters and associations. I have applied the Gaia data to the Taurus star-forming region, refining the sample of known members and identifying candidates for undiscovered members. The resulting samples of members and candidates provide the best constraints to date on the distribution of ages and the initial mass function (IMF) in Taurus. Several studies over the last 30 years have proposed the existence of a population of older stars (>~10 Myr) that is associated with the Taurus clouds. The data from Gaia demonstrate that such a population does not exist. Meanwhile, previous IMF estimates for small fields surrounding the Taurus aggregates have exhibited a surplus of K7-M0 stars (0.7-0.8 M_{sun}_) relative to star-forming clusters such as IC 348 and the Orion Nebula Cluster. However, that difference disappears when the new census of the entire region is considered, which should be complete for spectral types earlier than M6-M7 at A_J_<1. Thus, there is little variation in the stellar IMF across the 3-4 orders of magnitude in stellar density that are present in nearby star-forming regions. Finally, I note that the proper motions of two previously known members, KPNO 15 and 2MASS J04355209+2255039, indicate that they may have been ejected from the same location within the L1536 cloud ~7200 years ago.