(Not so) hierarchical stellar multiples seen through the eyes of Kepler, TESS, and other missions

During the era of Kepler, TESS, and other related star-monitoring space-based missions, quasi-continuous observations of thousands of known and previously unknown eclipsing binaries for several months (or even years) has led to the discovery of hundreds of compact hierarchical triple (and multiple) star systems. Many of them produce spectacular observational effects that were never (or at least, rarely) seen before, for example: extra outer eclipses; third-body perturbation-dominated, large amplitude, non-sinusoidal eclipse timing variations; rapid eclipse depth variations, etc. Successful modeling of these phenomena is a great challenge; however, it does offer substantial astrophysical benefits. In this paper we review our two different approaches to these challenges: one of them is based on the analytical theory of third-body perturbations and is applied exclusively to the eclipse timing variations, while the other is a complex, numerical, spectro-photodynamical modeling of all the available observations of such systems. We discuss some recent results obtained for TESS systems.