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In the last decades, 3D city models appear to have been predominantly used for visualisation; however, today they are being increasingly employed in a number of domains and for a large range of tasks beyond visualisation. In this paper, we seek to understand and document the state of the art regarding the utilisation of 3D city models across multiple domains based on a comprehensive literature study including hundreds of research papers, technical reports and online resources. A challenge in a study such as ours is that the ways in which 3D city models are used cannot be readily listed due to fuzziness, terminological ambiguity, unclear added-value of 3D geoinformation in some instances, and absence of technical information. To address this challenge, we delineate a hierarchical terminology (spatial operations, use cases, applications), and develop a theoretical reasoning to segment and categorise the diverse uses of 3D city models. Following this framework, we provide a list of identified use cases of 3D city models (with a description of each), and their applications. Our study demonstrates that 3D city models are employed in at least 29 use cases that are a part of more than 100 applications. The classified inventory could be useful for scientists as well as stakeholders in the geospatial industry, such as companies and national mapping agencies, as it may serve as a reference document to better position their operations, design product portfolios, and to better understand the market.