Abstract: In this talk we propose functional a posteriori error estimates for the boundary element method (BEM) together with a related adaptive mesh-refinement strategy. Unlike most a posteriori BEM error estimators, the proposed functional error estimators are independent of the discretization of the boundary integral equation and, more importantly, do not control the error in the integral density on the boundary, but rather the error of the potential approximation in the domain, which is of greater physical relevance. The estimators rely on the numerical solution of auxiliary problems on strip domains along the boundary, and are based on the boundary residual resulting from BEM. We will present the adaptive algorithm driven by functional error estimators and give a sketch of the convergence proof, which relies heavily on additional elliptic regularity of the solutions of the auxiliary problems. Numerical experiments are presented in order to illustrate the theoretical results.