This chapter focuses on the tessellation, tiling, and weaving of architectural surfaces. These three processes produce a geometric pattern of interconnected shapes that cover a plane. In architecture, such techniques are usually employed to create a more durable or weather-resistant finish for a floor, wall, or ceiling. They also serve as a means of decorating a surface to achieve an esthetic, poetic, or symbolic effect, some of which are used to evoke mathematical properties. This chapter offers an overview of the development of architectural tiling, emphasizing important links to mathematics. The architectural examples range from simple Neolithic weaving and stonecutting practices to late twentieth-century aperiodic cladding systems in prominent public buildings. The chapter also references past research into tiling in architecture and the main themes that have been explored previously.