Shape grammars are one of the main generative design algorithms. The theories and practices of shape grammars have developed and evolved over four decades and have had a significant impact on design computation and contemporary architecture. The formal computational approach to generative design as specified in shape grammars and the novel descriptions and applications of shapes and shape rules for representing and composing a design have become the foundation and inspiration for many contemporary computational design methods and tools—especially parametric design which is a current leading computational design method. This chapter gives an overview of the historical developments and applications of shape grammars. The algorithm is introduced by highlighting the background, key components and procedures for design generation, methods and issues for authoring shape grammars, shape grammar evolution and extension, application of shape grammar, and implementations of shape grammar. The characteristics of shape grammars are presented and discussed by comparing them to other key generative design algorithms, some of which have been applied in conjunction with shape grammars. This chapter shows that shape grammars have significant potential for design generation, analysis, and optimization, as seen in many of the grammar studies. The future directions should focus on further research, improved pedagogy, as well as validation in design practice, to further advance the field.