The decarbonization of the electricity grid as one among the actions to reduce fossil fuel emissions, and thus their impact on global warming in the future, will be achieved mainly via the integration and widespread diffusion of renewable power sources. This is going to be supported also by the shift from the paradigm production-transmission-distribution, where electricity production oversees large-size power plants, to renewable-based distributed/diffused production, where electricity is generated very close or even by the same (group of) user(s) (or prosumers in the latter case). The number of mid-/small-size installations based on renewable energy technologies will therefore increase substantially, and the related renewable generation will be dominant against that from large-size power plants. Unfortunately, this will reduce the reliability of the grid very likely, unless appropriate countermeasures are taken/implemented, hopefully at the same time the paradigm shift is being achieved. To this aim, it is important to identify the anomalies and main fault causes that might determine in renewable-based power systems. This paper surveys the current state-of-the-art on anomalies and faults affecting wind-PV-storage hybrid power systems, i.e., the main renewable technology ensemble that will establish the future grid, and highlights possible research directions that may help to fill the literature gaps.