  Let $\Omega \subset \mathbb{R}^{n+1}$, $n\geq 2$, be 1-sided NTA domain (aka
uniform domain), i.e. a domain which satisfies interior Corkscrew and Harnack
Chain conditions, and assume that $\partial\Omega$ is $n$-dimensional
Ahlfors-David regular. We characterize the rectifiability of $\partial\Omega$
in terms of the absolute continuity of surface measure with respect to harmonic
measure. We also show that these are equivalent to the fact that
$\partial\Omega$ can be covered $\mathcal{H}^n$-a.e. by a countable union of
portions of boundaries of bounded chord-arc subdomains of $\Omega$ and to the
fact that $\partial\Omega$ possesses exterior corkscrew points in a qualitative
way $\mathcal{H}^n$-a.e. Our methods apply to harmonic measure and also to
elliptic measures associated with real symmetric second order divergence form
elliptic operators with locally Lipschitz coefficients whose derivatives
satisfy a natural qualitative Carleson condition.
