Architecture has been indebted to geometric surfaces since ancient times, as books of descriptive geometry are witness: “Any architectonic creation is Geometry”. However, such geometries have evolved from classical surfaces to those designed with the help of a new discipline: Computer Aided Geometric Design (CAGD). The author reviews pre-computer geometric design exemplified by the use of hyperbolic paraboloids (Gaudí and Candela), its origin in the automotive industry and how it has been used brilliantly by Gehry in the Guggenheim Museum, Bilbao.