Abstract Photovoltaics (PV) has recently undergone impressive growth and substantial cost decreases, while deployment for concentrating solar power (CSP) has been much slower. As the share of PV rises, the challenge of system integration will increase. This favors CSP, which can be combined with thermal storage and co-firing to reduce variability. It is thus an open question how important solar power will be for achieving climate mitigation targets, and which solar technology will be dominant in the long-term. We address these questions with the state-of-the-art integrated energy-economy-climate model REMIND 1.5, which embodies an advanced representation of the most important drivers of solar deployment. We derive up-to-date values for current and future costs of solar technologies. We calculate a consistent global resource potential dataset for both CSP and PV, aggregated to country-level. We also present a simplified representation of system integration costs of variable renewable energies, suitable for large-scale energy-economy-models. Finally, we calculate a large number of scenarios and perform a sensitivity study to analyze how robust our results are towards future cost reductions of PV and CSP. The results show that solar power becomes the dominant electricity source in a scenario limiting global warming to 2 °C, with PV and CSP together supplying 48% of total 2010–2100 electricity. Solar technologies have a stabilizing effect on electricity price: if both solar technologies are excluded in a climate policy scenario, electricity prices rise much higher than in the case with full technology availability. We also analyze the competition between PV and CSP: PV is cheaper on a direct technology basis and is thus deployed earlier, but at high supply shares the PV integration costs become so high that CSP gains a competitive advantage and is rapidly developed, eventually overtaking PV. Even in the most pessimistic scenario of our sensitivity study with no further cost reductions, CSP and PV still supply 19% of 2010–2100 electricity. We conclude that if a stringent climate target of 2 °C is to be met cost-efficiently, solar power will play a paramount role in the long-term transformation of the electricity system.