  I 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. This report focuses on the strategy and the challenges of
fully non-perturbative investigations in the B-meson sector, where the b-quark
is treated within an effective theory, as followed by the ALPHA Collaboration.
As an application, I outline its use to determine the b-quark mass and
summarize the status of our ongoing project in the two dynamical flavour
theory.
