Abstract: Boundary element methods (BEM) are a way to numerically solve elliptic boundary value problems by reformulating them as singular integral equations on the boundary of the domain, and by applying finite element (FEM) type methods to the resulting integral equations. This is very convenient and leads to potentially efficient computational schemes since now the unknown function lives on a manifold with dimension one less than that of the original domain. However, in order to arrive at an efficient working computer code that is backed up by a sound mathematical theory, one has to overcome some major algorithmic and analytic hurdles, in addition to the problems encountered in the corresponding FEM setting. Although most of these hurdles have been successfully attacked so that the whole situation is about as satisfactory as with FEM, there still remains a few glaring exceptions including the convergence theory of adaptive BEM. The difficulties are related to the non locality of the involved integral operators and fractional order Sobolev norms. For instance, geometric error reduction for adaptive BEM has been rigorously established so far only under the so-called saturation assumption, whereas the first such proof without saturation assumption for an adaptive FEM in 2D was published in 1996. This work is an attempt to fill this gap by developing a set of techniques that is able to prove geometric error reduction and quasi-optimal convergence rates for adaptive BEM, without relying on saturation type assumptions. The main ingredients of the proof are some new results on local a posteriori error estimates for boundary element methods, and an inverse-type inequality involving boundary integral operators on locally refined finite element spaces.