  I present analyses of semileptonic $B_c$ decays. I first discuss the decays
induced by $c \to \{s, d \}$ transitions, in particular $B_c \to B_a \,
\bar{\ell} \, \nu_\ell$ and $B_c \to B_a^*(\to B_a \, \gamma) \, \bar{\ell} \,
\nu_\ell$ decays, with $a = \{s, d \}$ and $\ell = \{ e, \mu \}$, in the
Standard Model and in the extension based on the low-energy Hamiltonian
comprising the full set of $D = 6$ semileptonic $c \to s, d$ operators with
left-handed neutrinos.\\ Moreover, I consider $b \to c$ modes, with particular
focus on the determination of the form factors parametrizing the $B_c \to
J/\psi,\eta_c$ matrix elements of the operators in a generalized low-energy $b
\to c$ semileptonic Hamiltonian. In this case I consider an expansion in
nonrelativistic \qcd\ together with an expansion in the inverse heavy-quark
mass which allows the form factors to be expressed in terms of universal
functions in a selected kinematical range.\\ The Heavy Quark Spin Symmetry is
used for both analyses. In the first case, it allows the relevant hadronic
matrix elements to be related and the lattice \qcd\ results on $B_c$ form
factors to be exploited. Optimized observables are selected, and correlations
among them is studied to identify the effects of the various operators in the
extended low-energy Hamiltonian. In the second one, using as an input the
lattice \qcd\ results for the $B_c \to J/\psi$ matrix element of the Standard
Model operator, it is possible to obtain information on other form factors. The
extrapolation to the full kinematical range is also presented.
