With TESS we have discovered about a dozen new triply eclipsing triple stars, i.e., hierarchical triple or multiple stellar systems where the outer stellar component recurrently eclipses the inner eclipsing binary or is eclipsed by it. The outer orbital periods of these systems were found to be between 1.5 months and ~1 year, and therefore, in most cases, the orbits of the EBs depart significantly from simple Keplerian motion which is manifested by strong eclipse timing variations (ETVs). For a few case studies we present the full process of studying such systems beginning with their identification through an initial characterization of the `third body' eclipses, to follow-up ground-based observations and the use of archival data, and then to the final complex photodynamical modelling. The latter includes joint (multi-epoch, multi-band) lightcurve, ETV curve, radial velocity curve (if available), and composite SED analyses. Such studies can allow for the complete characterization of the system parameters, including the detailed orbital architecture. A surprising number of overall flat systems have been found.

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