  We determine {\`a} la Landau the critical velocity $v\_c^{L}$ of a moving
impurity in a Fermi superfluid, that is by restricting to the minimal
excitation processes of the superfluid. $v\_c^{L}$ is then the minimal velocity
at which these processes are energetically allowed. The Fermi superfluid
actually exhibits two excitation branches~: one is the fermionic pair-breaking
excitation, as predicted by BCS theory; the other one is bosonic and sets pairs
into motion, as predicted by Anderson's RPA. $v\_c^{L}$ is the smallest of the
two corresponding critical velocities $v\_{c,f}^{L}$ and $v\_{c,b}^{L}$. In the
parameter space (superfluid interaction strength, fermion-to-impurity mass
ratio), we identify two transition lines, corresponding to a discontinuity of
the first-order and second-order derivatives of $v\_c^{L}$. These two lines
meet in a triple point and split the plane in three domains. We briefly extend
this analysis to the very recently realized case at ENS, where the moving
object in the Fermi superfluid is a weakly interacting Bose superfluid of
impurities, rather than a single impurity. For a Bose chemical potential much
smaller than the Fermi energy, the topology of the transition lines is
unaffected; a key result is that the domain $v\_c^{L}=c$, where $c$ is the
sound velocity in the Fermi superfluid, is turned into a domain
$v\_c^{L}=c+c\_B$, where $c\_B$ is the sound velocity in the Bose superfluid,
with slightly shifted boundaries.
