Origami has emerged as a tool for designing three-dimensional structures from flat films. Because they can be fabricated by lithographic or roll-to-roll processing techniques, they have great potential for the manufacture of complicated geometries and devices. This article discusses the mechanics of origami and kirigami with a view toward understanding how to design self-folding origami structures. Whether an origami structure can be made to fold autonomously depends strongly on the geometry and kinematics of the origami fold pattern. This article collects some of the results on origami rigidity into a single framework, and discusses how these aspects affect the foldability of origami. Despite recent progress, most problems in origami and origami design remain completely open.

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