Origami, an ancient art of folding paper into structures, has inspired engineering applications in space technology a few decades ago. Due to rapid developments in manufacturing and construction technologies in recent years, scientists and engineers across the world are exploring the use of origami for applications in many other fields including mechanical, biomedical, robotics, and architecture. The property of origami-inspired structures to be lightweight, to be able to fold into compact volumes and be able to deploy into large structures can have applications for emergency shelters, deployable bridges, and may be even foldable houses or buildings. In this paper, recent developments and studies on origami-inspired futuristic structures for civil engineering and architecture are reviewed. The current state-of-the-art and the scope for development is discussed. Load-bearing capabilities of origami-based structures are analyzed. Alternative uses of origami concepts to design novel systems called metamaterials, which can have applications in vibration control or blast mitigation, are discussed.