Most Integrated Assessment Models (IAMs) have underestimated the role that solar PV can play in future low-carbon energy systems. This is critical as IAMs results constitute the main scenarios included in the Assessment Reports of the Intergovernmental Panel on Climate Change (IPCC). In this review, we discuss the main reasons behind the underestimation of solar PV and compare IAMs results with those provided by energy models using high spatial and temporal resolution. We include a call for action for improving IAMs and changing the paradigm regarding the role that solar PV can play to mitigate climate change. We also identify the challenges for a sustained scaling up of solar PV in the next decade and provide recommendations.