  Given any field $k$ (not necessarily perfect), we study the smoothing of a
semistable Fano variety over $k$. In characteristic 0, the reduced semistable
Fano degenerate fibers of Mori fibrations are classified. In positive
characteristic, under a suitable $W_2$ lifting assumption, we prove that a
semistable Fano variety always appears as a degenerate fiber in a semistable
family if it has a global log structure (in the sense of Fontaine-Illusie-Kato)
of semistable type. A similar smoothing result over a mixed characteristic base
is also obtained.
