Transit Timing and Duration Variations for the Discovery and Characterization of Exoplanets in the TESS era

Transiting exoplanets in multi-planet systems have non-Keplerian orbits which can cause the times and durations of transits to vary. The theory and observations of transit timing variations (TTV) and transit duration variations (TDV) are reviewed. The Kepler spacecraft has detected several hundred perturbed planets, many of which are still undergoing further study, and now TESS is adding to this sample. In a few cases, these data have been used to discover additional planets, similar to the historical discovery of Neptune in our own Solar System. However, the more impactful aspect of TTV and TDV studies has been characterization of planetary systems in which multiple planets transit. After addressing the equations of motion and parameter scalings, the main dynamical mechanisms for TTV and TDV are described, with citations to the observational literature for real examples. Constraints on model parameters from timing are elucidated, particularly the origin of the mass/eccentricity degeneracy and how it is overcome by the high-frequency component of the signal. On the observational side, derivation of timing precision and introduction to the timing diagram are given. Science results are reviewed, with an emphasis on mass measurements in multi-transiting planetary systems, from which bulk compositions may be inferred. The progress being made in studying transit timing with TRAPPIST-1 and TESS multi-planet systems is reviewed, as well as what the future may hold.