  In this paper we study the free boundary regularity for almost-minimizers of
the functional \begin{equation*} J(u)=\int_{\mathcal O} |\nabla u(x)|^2
+q^2_+(x)\chi_{\{u>0\}}(x) +q^2_-(x)\chi_{\{u<0\}}(x)\ dx \end{equation*} where
$q_\pm \in L^\infty(\mathcal O)$. Almost-minimizers satisfy a variational
inequality but not a PDE or a monotonicity formula the way minimizers do (see
[AC], [ACF], [CJK], [W]). Nevertheless we succeed in proving that, under a
non-degeneracy assumption on $q_\pm$, the free boundary is uniformly
rectifiable. Furthermore, when $q_-\equiv 0$, and $q_+$ is H\"older continuous
we show that the free boundary is almost-everywhere given as the graph of a
$C^{1,\alpha}$ function (thus extending the results of [AC] to
almost-minimizers).
