Abstract: We will discuss the long-time dynamics of the derivative nonlinear Schrodinger equation. For small, localized initial data, where no solitons arise, we prove dispersive estimates globally in time.  Under the same assumptions, we further prove modified scattering and asymptotic completeness. To the best of our knowledge, this is the first result to achieve an asymptotic completeness theory in a quasilinear setting. Our approach combines the method of testing by wave packets of Ifrim and Tataru, a bootstrap argument, and the Klainerman–Sobolev vector field method.