Origami (paperfolding) has greatly progressed since its first usage for design of cult objects in Japan, and entertainment in Europe and the USA. It has now entered into artistic areas using many other materials than paper, and has been used as an inspiration for scientific and engineering realizations. This article is intended to illustrate several aspects of origami that are relevant to engineering structures, namely: geometry, pattern generation, strength of material, and mechanisms. It does not provide an exhaustive list of applications nor an in-depth chronology of development of origami patterns, but exemplifies the relationships of origami to other disciplines, with selected examples.