Origami‐based designs refer to the application of the ancient art of origami to solve engineering problems of different nature. Despite being implemented at dimensions that range from the nano to the meter scale, origami‐based designs are always defined by the laws that govern their geometrical properties at any scale. It is thus not surprising to notice that the study of their applications has become of cross‐disciplinary interest. This article aims to review recent origami‐based applications in engineering, design methods and tools, with a focus on research outcomes from 2015 to 2020. First, an introduction to origami history, mathematical background and terminology is given. Origami‐based applications in engineering are reviewed largely in the following fields: biomedical engineering, architecture, robotics, space structures, biomimetic engineering, fold‐cores, and metamaterials. Second, design methods, design tools, and related manufacturing constraints are discussed. Finally, the article concludes with open questions and future challenges. This article reviews the state of the art of origami‐based applications in engineering. Publications of origami‐based applications are reviewed according to the following fields: biomedical engineering, architecture, robotics, space structures, biomimetic engineering, fold‐cores, and metamaterials. Design methods and tools are also reviewed. Manufacturing considerations are provided and future challenges discussed.