New possibilities offered by recent modelling software allow the design of organic shapes that are appealing to architects and engineers but may encompass serious issues such as an overconsumption of materials. In this context, there is a renewed interest in systems allowing the materialization of curved surfaces such as timber gridshells, which can be defined as shells with their structures concentrated in strips. However, gridshell design becomes highly challenging if complex grid configurations and new material possibilities are combinedly explored with form generations. These upheavals highlight the need for a classification system to seize the potential and the limitations of timber gridshells to address complex geometries. The classification of 60 timber gridshells enables a critical examination in the course of the ceaseless quest for complexity in architecture by evaluating current building possibilities and predict future building opportunities in terms of form, structure, and materiality.