Microassembly based on origami, the Japanese art of paper folding, presents an attractive methodology for constructing complex three-dimensional (3D) devices and advanced materials. A variety of functional structures have been created using patterned metallic, semiconducting, and polymeric thin films, but have been limited to those that curve in a single direction. We report a design framework that can be used to achieve spontaneous bidirectional folds with any desired angle, and we demonstrate theoretical and experimental realizations of complex 3D structures with +90 degrees , -90 degrees , +180 degrees , and -180 degrees folds. The strategy is parallel, versatile, and compatible with conventional microfabrication.