Several contemporary architectural works are arguing use of parametric design technologies, without clearly identifying their essential conditions. This article reviews meanings of this term and its first literary uses in referring to architectural design, as well as initial works applying these techniques, with the purpose of clarifying its original sense and applications, to support a consistent development. The word has different meanings ranging from social to mathematical connotations, mostly related to a measurable variation. Meanwhile, the documents about architectural works consider the concept of parametric design from the stand point of management of building information to specific geometric operations. The works reviewed as early examples of parametric procedures in building design are the Philips Pavilion by Le Corbusier and Xenakis, the Barcelona Fish by Frank Gehry and the Extension of Waterloo Station by Nicholas Grimshaw. It comments on their general process of production, functional and construction issues involved in the design of these three cases. Geometrical and computer procedures are described in relation to shape definition, structural solution and design expression of each building. Based on the texts and cases reviewed, the article suggests a strict conception of parametric design in architecture, linked to variable curves, as well as a constructive and cultural sense.