We will discuss experiments on the fundamental interplay of geometry, elasticity, and applied boundary conditions in determining the shape transformation of slender elastic materials. A thin sheet under a subtle combination of tension and twist can transform into a rich variety of shapes including helicoids, triangular folds, tubes, scrolls, and self-wrapped ordered and crumpled structures depending on the aspect ratio. After reviewing the primary wrinkling instabilities, and the far-from-threshold approach needed to explain their features, we will discuss the further development of ordered structure with origami, and a string model of the observed sawtooth torque response. We will then examine the interaction between a set of uniform fibers which are twisted starting from a lattice arrangement. The appearance of defects and the evolution of bundle cross-section as a function of twist will be discussed with a non-Euclidean model of the fiber structure in the bendable but inextensible limit. The importance of the elasticity of the elements will be further highlighted by demonstrating the remarkable persistence of order when the fiber bundle is composed of Hookean elements.