The dynamics of a cantilevered elastic sheet, with a uniform steady flow impinging on its clamped end, have been studied widely and provide insight into the stability of flags and biological phenomena. Measurements show that reversing the sheet's orientation, with the flow impinging on its free-edge—producing an “inverted flag”—dramatically alters its dynamics. In contrast to the conventional flag, which exhibits (small-amplitude) flutter above a critical flow speed, the inverted-flag displays large-amplitude flapping over a finite band of flow speeds. In this talk, I will give an overview of our work on this canonical problem that uses a combination of mathematical theory, scaling analysis, direct numerical simulations, and measurement. Flapping is found to be a vortex-induced vibration and is periodic predominantly, with a transition to chaos as flow speed increases. The effect of sheet motion on vortex formation will also be explored. This work was motivated by energy generation using wind turbines. It also has broader implications to leaf motion, and other biological processes such as the dynamics of hairs, because they also can present an inverted-flag configuration.