In Western architecture, masonry and stonework vaults were the main structures used over the centuries for covering internal spaces of buildings. In specific historical periods (Middle Age, Baroque, until Contemporary...) the vaults take particular complexity due to a more stringent link between Geometry and Architecture that fuels the inventive abilities of designers and builders. The experimentation and the construction of new spatial configurations were favored by the virtuosic application of stereotomy for stone works or the enhancements of building techniques for masonry and concrete works. In particular, the study of vaulted systems involves the search of the relationships between Geometry and Architecture in the process from design to construction, dealing with shapes, materials, and ornamentations. The theme of this special issue encompasses complex vaulted systems over the centuries. Topics of interest include: - Modeling of historical sources about vaults’ geometry and architecture; - Morphologic comparative studies of geometrically-shaped vaults; - Analysis of geometric tracing, stereotomy, centering, and calculus methods in built-heritage; - Investigation on the relationships between geometry and structure in historicized vaulted systems.