Supermassive black holes have been a key element to explain the thermal emission of AGN by the gravitational energy released through gas accretion. When the large luminosities of many AGN were observed, which apparently shone brighter than allowed by the Eddington limit, directly proportional to the black hole mass, one had to assume that emission was produced in collimated relativistic outflows that are directed along the line of sight. This scenario also offered a reasonable scheme for the unification of the various classes of AGN, and allowed a significant relaxation of the constraints imposed by the variability of the detected non-thermal emission. However, through observations in the gamma-ray energy band, the most extreme variability timescales observed are now very close to the phenomenological limits. Thus, the paradigm of radiation beaming due to relativistic effects has been questioned and some non-conventional models, e.g., due to operation of vacuum gaps in the black-hole magnetosphere, are actively considered now. In this talk I will discuss the implications of very short variability measured in gamma rays in the framework of different scenarios. In particular, I will show the limitations of models that involve operation of vacuum gaps, magnetic reconnection, and interaction of the jet with obstacles.