Lang was born in Dayton, Ohio, and grew up in Atlanta, Georgia. Lang attended California Institute of Technology for his undergraduate work in electrical engineering, where he met his wife-to-be, Diane. He earned a Master's degree in electrical engineering from Stanford in 1983, and returned to Caltech to pursue a Ph.D. in Applied Physics with a dissertation titled “Semiconductor Lasers: New Geometries and Spectral Properties.”

Lang began work for NASA's Jet Propulsion Laboratory in 1988. Lang also worked as a research scientist for Spectra Diode Labs of San Jose, California, and then at JDS Uniphase, also of San Jose.

Lang has authored or co-authored over 80 publications on semiconductor lasers, optics, and integrated optoelectronics, and holds 46 patents in these fields.

In 2001, Lang left the engineering field to being a full-time origami artist and consultant. However, he still maintains ties to his physics background: he is the editor-in-chief of the Journal of Quantum Electronics and does part-time laser consulting for Cypress Semiconductor.

Lang currently resides in Alamo, California.

Lang was introduced to origami at the age of six by a teacher who had exhausted other methods of keeping him entertained in the classroom. By his early teens, he was designing original origami patterns. Lang used origami as an escape from the pressures of undergraduate studies. While studying at Caltech, Lang came into contact with other origami masters such as Michael LaFosse, John Montroll, Joseph Wu, and Paul Jackson through the Origami Center of America, now known as OrigamiUSA.

While in Germany for postdoctoral work, Lang and his wife were enamored of Black Forest cuckoo clocks, and he became a sensation in the origami world when he successfully folded one after three months of design and six hours of actual folding.

Lang takes full advantage of modern technology in his origami, including using a laser cutter to help score paper for complex folds.

Lang is recognized as one of the leading theorists of the mathematics of origami. He has developed ways to algorithmatize the design process for origami, and is the author of the proof of the completeness of the Huzita—Hatori axioms.

Lang specializes in finding real-world applications for the various theories of origami he has developed. These included designing folding patterns for a German airbag manufacturer. He has worked with the Lawrence Livermore National Laboratory in Livermore, California, where a team is developing a powerful space telescope, with a 100 m (328 ft) lens in the form of a thin membrane. Lang was engaged by the team to develop a way to fit the tremendous lens, known as the Eyeglass, into a small rocket in such a way that the lens can be unfolded in space and will not suffer from any permanent marks or creases.

Lang is the author or co-author of eight books and many articles on origami.