Leptonic Decays of Heavy Quarks on the Lattice

The status of lattice calculations of heavy-light decay constants and of the $B$ parameter $B_B$ is reviewed. After describing the lattice approach to heavy quark systems, the main results are discussed, with special emphasis on the systematic errors in present lattice calculations. A detailed analysis of the continuum limit for decay constants is performed. The implications of lattice results on studies of CP violation in the Standard Model are discussed.