  We convey an idea of the significant recent progress, which opens up good
perspectives for high-precision ab-initio computations in heavy flavour physics
based on lattice QCD. Rather than surveying the latest results, this
contribution focuses on the concept and the challenges of fully
non-perturbative computations in the B-meson sector, where the b-quark is
treated within an effective theory. We outline its use to determine the b-quark
mass and report on the results obtained in the quenched approximation and on
the status in the two dynamical flavour theory.
