  The symmetric projective varieties of rank one are all smooth and Fano by a
classic result of Akhiezer. We classify the locally factorial (respectively
smooth) projective symmetric $G$-varieties of rank 2 which are Fano. When $G$
is semisimple we classify also the locally factorial (respectively smooth)
projective symmetric $G$-varieties of rank 2 which are only quasi-Fano.
Moreover, we classify the Fano symmetric $G$-varieties of rank 3 obtainable
from a wonderful variety by a sequence of blow-ups along $G$-stable varieties.
Finally, we classify the Fano symmetric varieties of arbitrary rank which are
obtainable from a wonderful variety by a sequence of blow-ups along closed
orbits.
