  We present the new analysis of the semileptonic B decays in the framework of
the relativistic quark model based on the quasipotential approach. Decays both
to heavy D^{(*)} and light \pi(\rho) mesons are considered. All relativistic
effects are systematically taken into account including contributions of the
negative-energy states and the wave function transformation from the rest to
moving reference frame. For heavy-to-heavy transitions the heavy quark
expansion is applied. Leading and subleading Isgur-Wise functions are
determined as the overlap integrals of initial and final meson wave functions.
For heavy-to-light transitions the explicit relativistic expressions are used
to determine the dependence of the form factors on the momentum transfer
squared. Such treatment significantly reduces theoretical uncertainties and
increases reliability of obtained predictions. All results for form factors,
partial and total decay rates agree well with recent experimental data and
unquenched lattice calculations. From this comparison we find the following
values of the Cabibbo-Kobayashi-Maskawa matrix elements:
|V_{cb}|=(3.85\pm0.15\pm 0.20)*10^{-2} and
|V_{ub}|=(3.82\pm0.20\pm0.20)*10^{-3}, where the first error is experimental
and the second one is theoretical.
