Low luminosity AGN represent the vast majority of the 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 review the challenges that parsec-scale observations across the electromagnetic spectrum of some of the nearest ones are opening 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 (Prieto et al. 2016; Fernandez-Ontiveros et al. 2019).