  Many objects in nature and industry are wrapped in a thin sheet to enhance
their chemical, mechanical, or optical properties. There are similarly a
variety of methods for wrapping, from pressing a film onto a hard substrate, to
using capillary forces to spontaneously wrap droplets, to inflating a closed
membrane. Each of these settings raises challenging nonlinear problems
involving the geometry and mechanics of a thin sheet, often in the context of
resolving a geometric incompatibility between two surfaces. Here we review
recent progress in this area, focusing on highly bendable films that are
nonetheless hard to stretch, a class of materials that includes polymer films,
metal foils, textiles, graphene, as well as some biological materials.
Significant attention is paid to two recent advances: (i) a novel isometry that
arises in the doubly-asymptotic limit of high flexibility and weak tensile
forcing, and (ii) a simple geometric model for predicting the overall shape of
an interfacial film while ignoring small-scale wrinkles, crumples, and folds.
