It is possible that most galaxies host a black hole at the centre, most of the time this being in a relatively quiescent state. The so-called low luminosity Active Galactic Nuclei are characteristic of this phase. These objects represent the vast majority of the active galactic nuclei (AGN) population in the near universe, and still the least conforming class with the standard AGN scenario. Their low luminosity is at odds with their often very high black hole masses and powerful jets. I will present the challenges that parsec-scale observations across the electromagnetic spectrum of some of the nearest ones impose on the true nature of their emission, their transition from the most luminous to the feeble ones, and their accretion power. The strict limits imposed by these observations on their accretion power are confronted with the high mechanical energy inferred for their jets. Possible scenarios for these nuclei including the extraction of power form the black hole spin are discussed.