  In the heavy quark effective theory, hadronic matrix elements of currents
between two hadrons containing a heavy quark are expanded in inverse powers of
the heavy quark masses, with coefficients that are functions of the kinematic
variable $v\cdot v'$. For the ground state pseudoscalar and vector mesons, this
expansion is constructed at order $1/m_Q^2$. A minimal set of universal form
factors is defined in terms of matrix elements of higher dimension operators in
the effective theory. The zero recoil normalization conditions following from
vector current conservation are derived. Several phenomenological applications
of the general results are discussed in detail. It is argued that at zero
recoil the semileptonic decay rates for $B\to D\,\ell\,\nu$ and $B\to
D^*\ell\,\nu$ receive only small second order corrections, which are unlikely
to exceed the level of a few percent. This supports the usefulness of the heavy
quark expansion for a reliable determination of $V_{cb}$.
