In the United Kingdom (UK), recent developments in the construction industry have increased the demand for digitised infrastructure, which facilitates the investigation of the as-is performance of assets. This establishes the need to create and maintain up-to-date digital copies of infrastructure assets, often labelled as Digital Twins. Digital twins are obtained by converting the unstructured data formats of the real-world assets, such as point clouds, into high-level digital representations. Yet, only few assets today have usable digital twins because of the high costs of the latter. This counteracts the benefits of the twins and reduces dramatically their true potential. Hence, there is a pressuring need to automate the process of creating digital twins. Geometric digital twin, the most basic form of the twin, contains only the geometry of the physical asset. This paper reviews the work done in computer vision, geometry processing, and civil engineering fields to determine the potential that exists for automatically producing geometric digital twins of infrastructure.