Non-perturbative Heavy Quark Effective Theory: An application to semi-leptonic B-decays

We review a lattice strategy how to non-perturbatively determine the coefficients in the HQET expansion of all components of the heavy-light axial and vector currents, including 1/mh-corrections. We also discuss recent preliminary results on the form factors parameterizing semi-leptonic B decays at the leading order in 1/mh.