How can we design shape (for function)? I will describe a class of inverse problems in physical geometry inspired by this simple question in a few different settings. These include kirigami tilings for planar and three-dimensional shapes, origami tessellations for complex curved surfaces, and printing and growing strategies to create flowers and faces, using a combination of experimental, computational and theoretical approaches. Along the way I will show how we can also control the energy landscape of the resulting set of shapes by varying the connectivity of the underlying unit cells that allows us to go from completely floppy networks to rigid structures and even totimorphs – structures that have an infinite range of energetically equivalent shapes.