  We review recent results on global wellposedness and long-time behavior of
smooth solutions to the derivative nonlinear Schr\"{o}dinger (DNLS) equation.
Using the integrable character of DNLS, we show how the inverse scattering
tools and the method of Zhou for treating spectral singularities lead to global
wellposedness for general initial conditions in the weighted Sobolev space
$H^{2,2}(\mathbb{R})$. For generic initial data that can support bright
solitons but exclude spectral singularities, we prove the soliton resolution
conjecture: the solution is asymptotic, at large times, to a sum of localized
solitons and a dispersive component, Our results also show that soliton
solutions of DNLS are asymptotically stable.
