Generative Artificial Intelligence (AI) has pioneered new methodological paradigms in architectural design, significantly expanding the innovative potential and efficiency of the design process. This paper explores the extensive applications of generative AI technologies in architectural design, a trend that has benefited from the rapid development of deep generative models. This article provides a comprehensive review of the basic principles of generative AI and large-scale models and highlights the applications in the generation of 2D images, videos, and 3D models. In addition, by reviewing the latest literature from 2020, this paper scrutinizes the impact of generative AI technologies at different stages of architectural design, from generating initial architectural 3D forms to producing final architectural imagery. The marked trend of research growth indicates an increasing inclination within the architectural design community towards embracing generative AI, thereby catalyzing a shared enthusiasm for research. These research cases and methodologies have not only proven to enhance efficiency and innovation significantly but have also posed challenges to the conventional boundaries of architectural creativity. Finally, we point out new directions for design innovation and articulate fresh trajectories for applying generative AI in the architectural domain. This article provides the first comprehensive literature review about generative AI for architectural design, and we believe this work can facilitate more research work on this significant topic in architecture.