• Challenges when allocating environmental impacts of reused building components. • Case study of a commercial building with reused components. • Comparison of design with upstream reuse and design for downstream reuse. • Comparison of six impact allocation methods over three typical life cycles. • Environmental assessment issues when applying circular economy principles in construction. The building industry is responsible for 35 % of all solid waste in Europe and more than a third of greenhouse gas (GHG) emissions. To address this, applying circular economy principles to the building sector is crucial, for example by reusing building elements from demolition sites rather than extracting and producing new materials. However, most current life-cycle assessment (LCA) tools are not appropriate to evaluate the environmental impact of a building when its components originate from prior buildings and/or will be used in future unknown ones. Still, robust measurement is needed to demonstrate the benefits of reuse towards environmentally sustainable cities. This paper compares existing methodologies to quantify the global warming potential (GWP, expressed in kg CO2e /unit) of recycled/recyclable and reused/reusable products, selected within widely recognised standards, rating schemes, and academic studies, such as the cut-off method, the end-of-life method, the distributed allocation (PAS-2050) method, the Environmental Footprint method, the Degressive method and the SIA 2032 method. Based on these recognised approaches for assessing the GWP of products, new equations are written and applied to buildings with reused/reusable materials for each of the methods. The Kopfbau Halle 118 building (Winterthur, CH, 2021), which is designed with reclaimed elements from local demolition sites, is chosen as a case study. Discrepancies in LCA methods are highlighted by applying them to three different life cycles corresponding to the first, intermediate, or final use of building components. This paper shows that current quantification methods to assess reuse give wide-ranging results and do not address the full spectrum of the reuse practice, that their boundaries are too limited, and that a number of critical features are currently hardly quantifiable, such as embedded use value, versatility, storage and transformation impacts, user-owner separation, dis/re-mountability, or design complexity. [ABSTRACT FROM AUTHOR]