In this talk, I will outline a general computational approach for the design of functional geometry. The key step is to identify suitable geometric abstractions of physical properties that enable effective computations with high predictive accuracy. I will focus on two examples of this approach, one for interactive design of complex 3D shapes with 2D auxetic materials, the other for performative optimization of light re-directing surfaces. These studies illustrate how to leverage geometric insights, mathematical theory, and advanced algorithms to develop effective computational tools for material-aware design of performative geometry.