Conventional assembly of biosystems has relied on bottom‐up techniques, such as directed aggregation, or top‐down techniques, such as layer‐by‐layer integration, using advanced lithographic and additive manufacturing processes. However, these methods often fail to mimic the complex three dimensional (3D) microstructure of naturally occurring biomachinery, cells, and organisms regarding assembly throughput, precision, material heterogeneity, and resolution. Pop‐up, buckling, and self‐folding methods, reminiscent of paper origami, allow the high‐throughput assembly of static or reconfigurable biosystems of relevance to biosensors, biomicrofluidics, cell and tissue engineering, drug delivery, and minimally invasive surgery. The universal principle in these assembly methods is the engineering of intrinsic or extrinsic forces to cause local or global shape changes via bending, curving, or folding resulting in the final 3D structure. The forces can result from stresses that are engineered either during or applied externally after synthesis or fabrication. The methods facilitate the high‐throughput assembly of biosystems in simultaneously micro or nanopatterned and layered geometries that can be challenging if not impossible to assemble by alternate methods. The authors classify methods based on length scale and biologically relevant applications; examples of significant advances and future challenges are highlighted.