Twisted homophase bilayers, stacks of two rotated monolayers such as graphene, exhibit remarkable physical properties absent in their constituent monolayers. The structure of bilayer systems is dominated by a moiré effect and critically depends on the twist angle. Quiquandon & Gratias [Acta Cryst. (2025), A81, 94-106] develop a crystallographic framework for rigorous description of the structure of bilayers, including systems without a coincidence lattice. They offer a set of tools that can describe the structure of any arbitrary bilayer system and enable the connection with its physical properties.