The art of paper folding, known as origami, has transcended its artistic roots to become a key source of inspiration for science, engineering, and architecture – particularly in developing deployable, compact, and adaptable structures. These structures have proven versatility across several applications, from medical devices to the aerospace industry. In astronomy, deployable origami-inspired structures have been used in telescopes’ segmented mirrors that fold compactly for launch and unfold seamlessly in space; solar arrays that can be compressed into compact forms and expanded into large, efficient energy-harvesting structures; and satellite instruments, such as antennas, where efficient packaging and reliable deployment are the highest priorities. Deployable origami-based structures have also been explored in starshades to suppress unwanted starlight from a star, reconfigurable metasurfaces for dynamically manipulating electromagnetic waves, dynamic optical elements, and solar sails. Building on these applications, this study delves into origami engineering. At the core of origami engineering is the folding pattern, which defines the creases and structural behavior of the design. We identify and evaluate the most commonly used origami patterns in deployable structures, emphasizing their applications in space missions and astronomy. We restrict the analysis to patterns that are tessellable because they can approximate complex geometries, including planar, parabolic, and other curved surfaces. We simulate the behavior of these patterns under different conditions and analyze the mechanical and geometrical properties, kinematics, actuation loads, and resistance, providing a framework for selecting the most suitable one according to the specific requirements of each application. The applications of these origami-inspired systems are not limited to aerospace; they have the potential to revolutionize the design of deployable structures in multiple disciplines. However, their impact on astronomy is particularly significant. These systems offer efficient and versatile solutions to engineering challenges in extreme environments, enhancing portability, reconfigurability, stability, and sustainability in space exploration.