We investigate the dynamics of shape in growing systems - from bacteria to batteries - through the lenses of computational geometry, statistical mechanics, and soft matter physics, aiming to extract general principles of shape control. Living systems build remarkable structures (like you) with impressive robustness despite functioning in a wet, noisy environment. We imagine a future where the structures we use and live in can build and regulate their own complex morphology, the way biology does it. Our projects are baby steps in that direction, divided into three overlapping approaches:  Data-driven description of shape changes, model-driven understanding of shape control, and application-driven control of emerging shapes.