  We study the initial-boundary value problem for the derivative nonlinear
Schr\"odinger (DNLS) equation. More precisely we study the wellposedness theory
and the regularity properties of the DNLS equation on the half line. We prove
almost sharp local wellposedness, nonlinear smoothing, and small data global
wellposedness in the energy space. One of the obstructions is that the crucial
gauge transformation we use replaces the boundary condition with a nonlocal
one. We resolve this issue by running an additional fixed point argument.
  Our method also implies almost sharp local and small energy global
wellposedness, and an improved smoothing estimate for the quintic Schr\"odinger
equation on the half line. In the last part of the paper we consider the DNLS
equation on $\R$ and prove smoothing estimates by combining the restricted norm
method with a normal form transformation.
