Repeating transients in galactic nuclei: confronting observations with theory

In the last few years, a mysterious new class of astrophysical objects has been uncovered. These are spatially coincident with the nuclei of external galaxies and show X-ray variations that repeat on timescales of minutes to a month. They manifest in three different ways in the data: stable quasi-periodic oscillations (QPOs), quasi-periodic eruptions (QPEs) and quasi-periodic outflows (QPOuts). QPOs are systems that show smooth recurrent X-ray brightness variations while QPEs are sudden changes that appear like eruptions. QPOuts represent systems that exhibit repeating outflows moving at mildly-relativistic velocities of about 0.1-0.3c, where c is the speed of light. Their underlying physical mechanism is a topic of heated debate, with most models proposing that they originate either from instabilities within the inner accretion flow or from orbiting objects. There is a huge excitement especially from the latter class of models as it has been argued that some repeating systems could host extreme mass-ratio inspirals, potentially detectable with upcoming space-based gravitational wave interferometers. Consequently, paving the path for an era of "persistent" multi-messenger astronomy. Here we summarize the recent findings on the topics, including the newest observational data, various physical models and their numerical implementation.