Now that the amount of available experimental data is large as far as beauty physics is concerned, especially from LHC and B factories, precision tests of the Standard Model and trials of several New Physics scenarios are feasible in that area of flavour physics. Unfortunately the theoretical uncertainty, mainly coming from hardly computable long-distance effects of the strong interaction that confines quarks and gluons within hadrons, is potentially limiting the impact of future experimental measurements on New Physics models. Lattice QCD offers a powerful approach to compute these non-perturbative hadronic contributions; however some care is needed to obtain reliable results for b quark physics because one has to keep under control simultaneously the finite-size effects and the discretisation effects that are particularly severe when such a heavy quark is simulated. After having introduced the main features of lattice QCD and hints of heavy flavour physics, I will present a strategy to deal with the heavy quark on the lattice: it is based on Heavy Quark Effective Theory, paying attention to excited states, and illustrate it on a recent measurement of the b quark mass and the B meson decay constant.
