  Dispersion approach based on the constituent quark picture and its
applications to weak decays of heavy mesons are reviewed. Meson interaction
amplitudes are represented within this approach as relativistic spectral
integrals over the mass variables in terms of the meson wave functions and
spectral densities of the corresponding Feynman diagrams. Various applications
of this approach are discussed:
  Relativistic spectral representations for meson elastic and transition form
factors at spacelike momentum transfers are constructed. Form factors at
$q^2>0$ are obtained by the analytical continuation. As a result of this
procedure, form factors are given in the full $q^2$ range of the weak decay in
terms of the wave functions of the participating mesons.
  The 1/m_Q expansion of the obtained spectral representations for the form
factors for the particular limits of the heavy-to-heavy and heavy-to-light
transitions are analysed. Their full consistency with the constraints provided
by long-distance QCD for these limits is demonstrated. Predictions for form
factors for B, B(s), D, and D(s) decays to light mesons are given. The
B\to\gamma l\nu decay and the weak annihilation in rare radiative decays are
considered. Nonfactorizable corrections to the B^0-\bar B^0 mixing are
calculated. Inclusive weak B-decays are analysed and the differential
distributions are obtained in terms of the B-meson wave function.
