Almost ten years after their first use in the photovoltaic (PV) field, perovskite solar cells (PSCs) are now hybrid devices that, in addition to having reached silicon performance, can accelerate the energy transition and boost the use of abundant elements for their manufacturing process. However, noble metals (in particular gold) represent the most typically used sources for back electrode fabrication, and this issue has been intensively considered by the research community in the last five years. This review shows how the most promising solution, considering also the need to develop a large-scale production process, is based on the use of carbon-based materials for the preparation of back electrodes. Graphite, carbon black, graphene and carbon nanotubes (CNTs) have been proposed, functionalized and characterized, leading to laboratory-scale solar cells and modules capable of providing excellent efficiencies and ensuring stability greater than those of gold-based devices. Strengthened by these results and its hydrophobizing properties, carbon has also started to be used as an electron transporting material (ETM), with excellent results on both rigid and flexible substrates. This review discusses the major advances and the updated state-of-the-art in the carbon-based PSC scenario, keeping a solid trajectory where the accessibility, low cost, high electrical conductivity, chemical stability and controllable porosity of carbon are highlighted and exploited in the design of upscalable hybrid solar cells.