Abstract: Architectural geometry, as an emerging interdisciplinary research field, aims to address geometric challenges encountered throughout architectural design and fabrication processes. It bridges multiple disciplines, including architecture, geometry, engineering, and computer science. This paper systematically reviews the research progress in the field of architectural geometry, with a particular focus on the significant advantages of quadrilateral mesh-based discrete modeling in architectural design and construction. It also briefly introduces relevant studies involving other mesh types such as triangular and hexagonal meshes. The discussion centers on recent advances in discrete surface modeling, structural support systems, and design methodologies oriented toward fabrication. Furthermore, the article analyzes the applicability and limitations of existing research in terms of discretization modeling and manufacturability. It highlights the developmental trend of architectural geometry towards a deeper integration of geometric modeling with digital construction and intelligent fabrication, aiming to promote the intelligent transformation of the architectural design and fabrication pipeline. This work offers a valuable reference for future research in the field.