Some plants develop an ability to perform rapid motions (Venus flytraps, exploding Jewelweed seeds, etc.) even without muscles. They achieve this by manipulating the curvature of tissues to take advantage of the relationship between strains and geometry to trigger rapid conformational changes from one state to another. I will discuss a theoretical framework for designing snapping structures by taking advantage of ideas from origami. In particular, we create shells that can be folded along prescribed curves. Depending on the geometry of those folds, the fold can be actuated continuously or discontinuously through a snap-through transition. Beyond this, I will discuss how elasticity theory modifies this simple geometrical rule.