Geometry updating for digital twins of buildings is a time-consuming and manual task, resulting in poor progress monitoring and quality control during the construction stage. This paper reviews the state of the art in practice and research on spatial and visual data-based approaches for updating digital twin geometry of buildings. We draw novel key insights into the effectiveness, experiments, and limitations of seven classes of methods summarised from the most recent papers. Consequently, four core gaps in knowledge are investigated. Finally, a new geometry-based object class hierarchy is derived to support geometry updating for maintaining digital twins in future directions.