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Let $$ \Omega \subset \mathbb{R}^{n+1}$$, $$ n\geq 2$$, be a 1-sided NTA domain (also known as a 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.