Origami, an ancient art of paperfolding, has evolved beyond its traditional use for cultural and entertainment purposes and has found its way into artistic, scientific, and engineering realms. This research paper explores the mathematical foundations of origami, and later focuses on a specific application in biomedical engineering. This study is intended to illustrate several aspects of origami that are relevant to engineering structures, namely: geometry, pattern generation, flat-foldability, and the ability of origami tessellations to fit specific target shapes. This review further examines DNA Origami Nano-structures (DONs) which provide numerous benefits, including lower biotoxicity, increased stability, and superior adaptability, making them an excellent choice for Drug Delivery Systems.