The construction sector represents one of the most significant sources of waste generation in the European Union (EU), with nearly one billion tonnes of construction and demolition waste annually. This sector also contributes a third of the annual EU greenhouse gas (GHG) emissions. Accordingly, construction represents one priority area for intervention within the EU Action Plan for the Circular Economy. Increasing resource efficiency through slowing, closing, and narrowing material and energy loops, is key to mitigating climate change. However, this review paper demonstrates that the analysis of links between circular economy solutions and climate change mitigation has been scarce, despite a recent sharp increase in related literature, with 20 articles (83%) published in 2018-2019. Slowing resource solutions have been the focus of the research and could bring up to 99% savings in GHG emissions per functional unit, where material reuse stands out as the most promising alternative. Closing resource solutions can reduce emissions by 30-50% per functional unit, but results are highly dependent on recycling efficiencies and transportation distances to recovery facilities. Solutions for narrowing resource loops can bring additional GHG savings, but they remain understudied. Despite the promising results for mitigating GHG emissions, this article argues that the circular economy solutions do not always result by default in emission reductions and that a case-by-case quantification is crucial. The implementation of these solutions should be accompanied with further methodological development, such as proper allocation procedures, accurate definition of the system boundaries and integration of forecasts.