Herein, we discuss the folding of highly compliant origami structures—“Soft Origami.” There are benefits to be had in folding compliant sheets (which cannot self-guide their motion) rather than conventional rigid origami. Example applications include scaffolds for artificial tissue generation and foldable substrates for flexible electronic assemblies. Highly compliant origami has not been contemplated by existing theory, which treats origami structures largely as rigid or semirigid mechanisms with compliant hinges—“mechanism-reliant origami.” We present a quantitative metric—the origami compliance metric (OCM)—that aids in identifying proper modeling of a homogeneous origami structure based upon the compliance regime it falls into (soft, hybrid, or mechanism-reliant). We discuss the unique properties, applications, and design drivers for practical implementation of Soft Origami. We detail a theory of proper constraint by which an ideal soft structure's number of degrees-of-freedom may be approximated as 3n, where n is the number of vertices of the fold pattern. Buckling and sagging behaviors in very compliant structures can be counteracted with the application of tension; we present a method for calculating the tension force required to reduce sagging error below a user-prescribed value. Finally, we introduce a concept for a scalable process in which a few actuators and stretching membranes may be used to simultaneously fold many origami substructures that share common degrees-of-freedom.