Greenhouse gas emissions from anthropogenic sources are believed to be the main cause of global warming and climate change. Furthermore, fossil fuels are forecasted to remain the dominant source of energy in the near future. Therefore, capture and sequestration of greenhouse gases and in particular carbon dioxide is likely to be a major pathway toward environmental protection and energy sustainability. Such clarity has stimulated an intense and diverse range of research into various capture and mitigation technologies, which race with global warming in real-time. Quantification of the performance improvement rates of these technologies can inform decision-makers’ long-term investment strategies, and help researchers to identify technical bottlenecks and research potential. The present research estimates the yearly performance improvement rate of CO2 capture, non-CO2 GHG capture, and GHG mitigation technologies, using a novel method based on patent data and the corresponding citation network. Our findings suggest that membrane-based, condensation/rectification-based, and adsorption-based carbon capture are the most promising technologies. Furthermore, the average CO2 capture technologies are likely to improve slightly faster than solar, wind, and battery technologies, indicating their important role in future electrical grids. Unfortunately, subterranean or submarine CO2 storage was identified as a slow-growing technological domain and potentially a bottleneck in the future sustainable carbon chain, which requires further efforts.