Mitigation-Process Integrated Assessment Models (MP-IAMs) are used to analyze long-term transformation pathways of the energy system required to achieve stringent climate change mitigation targets. Due to their substantial temporal and spatial aggregation, IAMs cannot explicitly represent all detailed challenges of integrating the variable renewable energies (VRE) wind and solar in power systems, but rather rely on parameterized modeling approaches. In the ADVANCE project, six international modeling teams have developed new approaches to improve the representation of power sector dynamics and VRE integration in IAMs. In this study, we qualitatively and quantitatively evaluate the last years’ modeling progress and study the impact of VRE integration modeling on VRE deployment in IAM scenarios. For a comprehensive and transparent qualitative evaluation, we first develop a framework of 18 features of power sector dynamics and VRE integration. We then apply this framework to the newly-developed modeling approaches to derive a detailed map of strengths and limitations of the different approaches. For the quantitative evaluation, we compare the IAMs to the detailed hourly-resolution power sector model REMIX. We find that the new modeling approaches manage to represent a large number of features of the power sector, and the numerical results are in reasonable agreement with those derived from the detailed power sector model. Updating the power sector representation and the cost and resources of wind and solar substantially increased wind and solar shares across models: Under a carbon price of 30$/tCO2 in 2020 (increasing by 5% per year), the model-average cost-minimizing VRE share over the period 2050-2100 is 62% of electricity generation, 24%-points higher than with the old model version.