Towards precision heavy flavour physics from lattice QCD

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.