  We review the works devoted to third and fifth harmonic susceptibilities in
glasses, namely $\chi$ (3) 3 and $\chi$ (5) 5. We explain why these nonlinear
responses are especially well adapted to test whether or not some amorphous
correlations develop upon cooling. We show that the experimental frequency and
temperature dependences of $\chi$ (3) 3 and of $\chi$ (5) 5 have anomalous
features, since their behavior is qualitatively different to that of an ideal
gas, which is the high-temperature limit of a fluid. Most of the works have
interpreted this anomalous behavior as reflecting the growth, upon cooling, of
amorphously ordered domains, as predicted by the general framework of Bouchaud
and Biroli (BB). We explain why most-if not all-of the challenging
interpretations can be recast in a way which is consistent with that of
Bouchaud and Biroli. Finally, the comparison of the anomalous features of
$\chi$ (5) 5 and of $\chi$ (3) 3 shows that the amorphously ordered domains are
compact, i.e., the fractal dimension d f is close to the dimension d of space.
This suggests that the glass transition of molecular liquids corresponds to a
new universality class of critical phenomena.
