There are times when it is desirable for devices to be stowed compactly, ``transported'' to the location of their desired use, and then deployed to another stable shape or configuration to perform their designed function. Origami-based mechanisms are beneficial in these cases due to their compact, folded nature and large deployments. Unlike traditional mechanical design, compliant mechanism and origami-based design approaches inherently have coupled characteristics, creating complex design problems. The research presented here discusses metrics, methods, and designs to aid in the design of origami-adapted and compliant mechanisms, focusing on the design case of deployable space systems. First, the hexagonal twist origami pattern is used to develop performance metrics for next-generation deployable space arrays. These are shown using five different thickness accommodation techniques. The concepts are demonstrated through two applications: a deployable reflectarray antenna and a LiDAR telescope. Second, a highly compact stowable deployment is presented with the Deployable Euler Spiral Connectors (DESCs). These are compliant deployable flexures that can span gaps between segments in a mechanism and then lay flat when under strain in a stowed position. Additionally, a metamaterial is shown based on the combination of Euler spiral flexures (ESFs) to provide unique behaviors difficult to obtain in traditional materials, such as high compactability, decoupled motion and stiffness, tailorable Poisson's ratio, and multi-directional deployment. Third, this work presents a method for creating hinge-like motion for origami-adapted mechanisms using internal membranes attached between rigid panels. The goal is to remove adhesive requirements, preserve panel volume for use as hard stops, and reduce parasitic motion experienced by other membrane joint types, while keeping the stress in the membrane below the stress limits. Lastly, specific applications and examples of each of the above are shown throughout the work with a specific chapter highlighting more concise examples of creating metrics to determine the best origami patterns and to create compatible hinges. The presented techniques stand to greatly benefit the origami-adapted mechanisms design community.