The Derivative Nonlinear Schrödinger equation arises as a long-wave, small amplitude model in the context of Magnetohydrodynamics for conducting fluids, when the Hall effect is taken into account in the Ohm’s law. A central property of this equation, discovered by Kaup and Newell in 1978, is that it is an integrable system, solvable through the inverse scattering method. I will show how inverse scattering may provide tools to address fundamental questions such as global existence and long-time behaviour of solutions for large data, asymptotic stability of solitons, and, more generally, the soliton resolution conjecture which refers to the property that, for large times, solutions decompose into a finite number of well-separated solitons, and a small dispersive part.