Thanks to fast learning and sustained growth, solar photovoltaics (PV) is today a highly cost-competitive technology, ready to contribute substantially to CO2 emissions mitigation. However, many scenarios assessing global decarbonization pathways, either based on integrated assessment models or partial-equilibrium models, fail to identify the key role that this technology could play, including far lower future PV capacity than that projected by the PV community. In this perspective, we review the factors that lie behind the historical cost reductions of solar PV and identify innovations in the pipeline that could contribute to maintaining a high learning rate. We also aim at opening a constructive discussion among PV experts, modelers, and policymakers regarding how to improve the representation of this technology in the models and how to ensure that manufacturing and installation of solar PV- can ramp up on time, which will be crucial to remain in a decarbonization path compatible with the Paris Agreement.