Thin elastic films can be found everywhere: they occur naturally (lipid membranes, viral capsids, plant leaves, epithelial tissues, seashells, etc.) and as man-made materials (paper, graphene, fabrics, concrete shells, etc.). Since their resistance to bending must obey purely geometric surface constraints, stress and geometry are intricately coupled, often leading to unexpected and very nonlinear responses to perturbations. Recent progress in theoretical and experimental approaches, as well as novel technological applications, have advanced the frontier of this field, but also brought challenging new problems into focus, to which this conference is dedicated. Examples of interest include extreme mechanics, the cross-talk between stress and geometry, fluctuations in and out of equilibrium, frustrated internal stresses, and wetting of deformable sheets. We strive for a highly multidisciplinary meeting, in which experimentalists, theorists, and numerical simulators explore open questions in both biological and man-made model systems, examine the promise of novel theoretical and numerical techniques, identify the current frontier of understanding, and speculate on what type of new ideas or tools might be needed to push it further.