Quasars (Quasi Stellar Objects, abbreviated as QSOs) are still nowadays, close to half a century after their discovery, objects which are not completel y understood. In this brief review a description of the pending problems, inconsistencies and caveats in the QSO's research is presented. The standard paradigm model based on the existence of very massive black holes that are responsible for the QSO's huge luminosities, resulting from to their cosmological redshifts, leaves many facts without explanation. There are several observations which lack a clear explanation, for instance: the absence of bright QSOs at low redshifts, a mysterious evolution not properly understood; the inconsistencies of the absorption lines, such as the different structure of the clouds along the QSO's line of sight and their tangential directions; the spatial correlation between QSOs and galaxies; and many others.