TESS has provided continuous, high-cadence, long-baseline photometry for over 200,000 stars as part of its ambitious planet-finding mission. This treasure trove of light curves has simultaneously enabled detailed time-domain astronomical studies of previously discovered planetary systems. Over the course of the two-year Primary Mission, we carried out a wide-ranging systematic light curve analysis of known transiting systems. By detecting visible-light phase curves, we placed constraints on such fundamental physical quantities as: (1) the planet’s dayside temperature and Bond albedo, through measurement of the secondary eclipse depth in the TESS band; (2) the efficiency of day-night heat recirculation, via the amplitude and phase shift of the planet’s atmospheric brightness modulation across the orbit; and (3) the response of the host star to the mutual star-planet gravitational interaction, which is expressed in the phase curve signal via Doppler boosting of the star’s light and ellipsoidal distortion of the stellar surface. In this talk, we provide an overview of the main results from the Primary Mission. We measured secondary eclipse depths and phase curve amplitudes for over 20 targets, including such benchmark systems as WASP-18 and KELT-9. In addition, we combined TESS-band eclipse measurements with Spitzer 3.6 and 4.5 micron secondary eclipse depths to obtain self-consistent dayside temperatures and optical geometric albedos. This growing body of uniform albedo measurements has revealed an emerging trend between increasing dayside temperature and increasing apparent geometric albedo for hot Jupiters, which may indicate reflected light from high-temperature condensates or systematic deviations from a blackbody emission spectrum. With TESS now in its Extended Mission, we consider possible avenues for follow-up intensive atmospheric characterization with future ground- and space-based facilities and discuss fruitful opportunities for further study as the telescope revisits these systems in the coming years.