B-physics from lattice gauge theory

We discuss the main issues in dealing with heavy quarks on the lattice and shortly present the different approaches used. We discuss a selection of computations covering first the b-quark mass and the B-(s) meson decay constants as the consolidated results (neglecting isospin breaking corrections). In the second part, we consider recent calculations of form factors for tree-level semileptonic decays with emphasis on the tensions between the results produced by different collaborations. We propose benchmark quantities and tests suited to investigate the origin of such tensions. Finally, we review computations of the bag parameters parameterising neutral meson mixing and provide an overview on a few recent developments in the field.