Recently, novel structures inspired by origami principles have emerged, leveraging their lightweight and foldable characteristics for diverse applications. These structures also exhibit higher strength and stiffness, making them suitable for structural applications. Consequently, the use of the origami approach for designing innovative structures with excellent energy absorption capabilities has been increasing in engineering fields. This paper provides a comprehensive overview of recent advances in the development of origami-inspired structures for energy absorption applications. The unique features and remarkable mechanical properties of various origami structures, including metamaterials, honeycombs, thin-walled tubes, and foldcores fabricated from metals, polymers, composites, and multi-materials under different loading conditions, are critically discussed. Initially, the performance evaluation indexes and loading conditions for energy absorption of origami structures are summarized. The paper then classifies various types of origami structures and examines their incorporation into crash boxes, thin-walled tubes, cellular lattices, metamaterials, and sandwich structures, discussing their deformation behavior and energy absorption capabilities under different loading conditions. Finally, future research directions on energy absorption in origami structures are discussed. This review offers a valuable platform for researchers and engineers to develop novel designs based on origami-inspired structures for energy absorption applications.