The document presents a thorough review of 29 existing urban material accounting methods used in research projects and academic literature to illustrate the multitude of methods that exist and provide a good understanding of them. The analysis identifies strengths and weaknesses of most accounting techniques informing the adapted sector-wide and urban circularity assessment methods that will be developed in the CityLoops project. This is followed by an overview of how the application of various methods has changed over time, informed by the analysis of 194 publications.