I will discuss recent results on free boundary problems for elliptic operators with variable coefficients. We consider divergence form operators $L_A = -\mathrm{div}(A\nabla)$, where $A$ is a uniformly elliptic matrix whose coefficients satisfy a Dini Mean Oscillation-type condition. Given two disjoint domains $\Omega_1, \Omega_2 \subset \mathbb{R}^{n+1}$ satisfying the capacity density condition, we study the geometry of their common boundary $F = \partial \Omega_1 \cap \partial \Omega_2$ through the behavior of the associated elliptic measures. We establish a \emph{quantitative two-phase free boundary} result: If, in every boundary ball, the elliptic measures $\omega_1, \omega_2$ satisfy a scale-invariant mutual absolute continuity condition of $A_\infty$-type, then a large portion of $F$ must be uniformly $n$-rectifiable. More precisely, we produce sets $\Sigma_B \subset F$ carrying positive elliptic measure from both sides, and in fact satisfying quantitative lower bounds in terms of the Hausdorff measure. This result extends the rectifiability theory for harmonic measure to the setting of elliptic operators with rough coefficients and is based on joint work with A. Merlo and C. Puliatti.