A new strategy has been introduced to exploit mechanical buckling for autonomic origami assembly of three-dimensional (3D) microstructures across a wide range of material classes, including soft polymers and brittle inorganic semiconductors, and length scales from nanometers to centimeters. The engineered folding creases are created through spatial variation of thickness in the initial two-dimensional structures. This scheme extends the previous buckling approach for 3D fabrication and enables a wide range of 3D topologies with levels of geometrical complexity significantly beyond those reported previously.