When exoplanetary transits are no longer periodic

Exoplanetary transits are the periodic dimming of stars caused by the crossing of a black and opaque disk (the planet) in front of them". In this talk I will review many of the ways in which the former sentence is wrong: planets are neither opaque, nor non-luminous or disk-like, and transits may be neither color-neutral, constant in depth, duration or even have constant period. I will briefly describe how each and every one of these variations can tell us something about the planet and/or its system.I will then focus on the non-periodicity of planetary transits known as transit timing variations (TTVs). I will discuss its observational and dynamical origins, and show examples of the challenges and opportunities brought about by this new and exciting field of exoplanet studies, including new analytical tools and ground-based observational opportunities