In this talk, I will highlight the previously underappreciated role of brain geometry in influencing brain function and regional organization. I will show that geometric eigenmodes derived from the brain's cortical and subcortical geometry accurately capture diverse experimental human functional magnetic resonance imaging (fMRI) data from spontaneous and task-evoked recordings. I will then show that the close link between geometry and function is explained by a dominant role of wave-like activity, and that wave dynamics can reproduce numerous canonical features of functional brain organization. I will also show that geometric eigenmodes can be used to develop a simple, hierarchical approach that mimics a putative generative process for regional organization. The approach can effectively parcellate any brain structure in any species, defining regions with more homogeneous anatomical, functional, cellular, and molecular properties than most existing parcellations in use today. Finally, I will show that the approach captures the essence of reaction-diffusion mechanisms that play an important role in shaping the foundations of regional organization through neurodevelopment.