This chapter presents the theoretical foundation of parametric design for design generation in architecture. Parametric design has been increasingly applied to architectural design in recent years. It is essentially a digital design method, which can be characterized by rule-algorithmic design and multiple-solution generation. Parametric design originates from generative design, which is a typical computational design approach based on rules or algorithms (e.g., in generative grammars or evolutionary systems). This chapter starts with a critical review of generative design, followed by the background, history and theory of parametric design, including various fundamental concepts and applications that underpin parametric design, and concludes with a discussion about the future development of parametric design and its impact on architecture and designers.