  We present the results of the application of the Dispersion Matrix approach
to semileptonic heavy-to-heavy and heavy-to-light $B$-meson decays. This method
allows to determine the hadronic form factors in a non-perturbative and
model-independent way. Starting from the available lattice results at large
values of the momentum transfer, we obtain the behaviour of the form factors in
their whole kinematical range without introducing any parameterization of their
momentum dependence. We will focus on the determination of the
Cabibbo-Kobayashi-Maskawa matrix elements $\vert V_{cb} \vert$ and $\vert
V_{ub} \vert$ through the analysis of $B \to D^{(*)} \ell \nu$, $B_s \to
D_s^{(*)} \ell \nu$, $B \to \pi \ell \nu$ and $B_s \to K \ell \nu$ decays. New
theoretical determinations of the Lepton Flavour Universality ratios relevant
for these transitions will be also presented, by focusing in particular on the
$R(D_{(s)}^{(*)})$ ratios.
