Wrapping air: A balloon constructed by G. I. Taylor to test his prediction for the shape of an axisymmetric parachute, circa 1919 (public domain).

Many objects are wrapped in thin sheets to contain, protect, or conceal the contents, from foil-wrapped candy to high-altitude helium balloons to a liquid droplet sealed inside a polymer film. This review explores the mechanics and geometry of thin elastic wrappers, which are essential to a wide variety of applications in mechanical, chemical, and aerospace engineering, and have spurred basic questions in soft matter physics and mathematics. The manuscript will appear in Annual Review of Condensed Matter Physics in March 2019; see the advance online edition here or the arXiv version here.