A recently developed mathematical folding theory has great value for deployable space structures and in situ manufacture of large beams, panels and cylinders. The new technology offers diverse capacity to design, manufacture, and self-assemble periodically folded sheet material. The range of materials includes many customized core materials for laminated panels, cellular habitat walls, structural beams, parabolic reflectors, and efficient truss systems that can be packaged ideally as a roll of sheet material and deployed in space by inflation or passive radiation. The algebraic linkage conditions on the deployment of a folded structure forms an over-constrained system of equations. The deployment kinetics are only possible due to engineered relationships between the neighboring facet geometry, and globally requires a uniform angular change in fold extension across the pattern. This implies that fixing an individual fold angle fixes all of the fold angles in its neighboring region. If the fold angles are all made rigid, then the entire structure is highly over-constrained and forms a very robust truss system. The goal is to introduce the technology by demonstrating the diversity of folding architectures that can be directly applied to deployable space structures, and by developing the associated design and simulation software to transfer this know-how to the engineering community.