Many observed triple systems in our universe are in a hierarchical configuration: two objects orbit each other in a relatively tight inner binary while the third object is on a much wider orbit. In this case, the secular approximation (i.e., phase-averaged, long-term evolution) can be applied, where the interactions between two non-resonant orbits are equivalent to treating the two orbits as massive wires. Thus, the orbits may change shape and orientation, on timescales longer than the orbital periods, but the semi-major axes are constant. This approximation has been proven to be very useful in many astrophysical contexts, from planetary to triple-star systems and even black holes.
I will discuss recent developments in that field and will show that hierarchical triple systems are richer and far more exciting than considered before. In particular, the tight orbit can reach extremely high eccentricities and undergo chaotic flips of its orientation. This behavior has important implications for the evolution of many systems, and I will present some seminal examples, such as retrograde hot Jupiters, blue stragglers, and black hole binaries.