Tracing the Past: English Medieval Vaults is an ongoing research project at the University of Liverpool. It aims to use contemporary digital techniques to investigate the design and construction of vaults in England during the Middle Ages. Starting in 2015, the project has focused on fourteen case studies from across the UK, featuring a wide variety of vault designs. Digital surveys of each site are conducted using terrestrial laser scanning, allowing us to generate highly accurate 3D models of the vaults. By analysing the geometry of these models, we attempt to understand the technical processes through which these historic works of architecture were designed and built by medieval masons.