A critical review of nonlinear optical properties of fullerenes is pre
sented. We explore structure property relationships for optical nonlin
earities of these unusual pi electron systems from two complementary a
ngles: (i) to explore the possibility of obtaining structural informat
ion from nonlinear optical experiments and (ii) to assess the potentia
l of fullerenes, fullerites and their derivatives for the practical no
nlinear optical devices. In particular we show that substituted fuller
enes form an interesting class of molecules for nonlinear optics. We w
ill also show that third harmonic generation of circularly polarised l
ight in the solid fullerites should yield some information on the inte
rmolecular interactions in these solids. We critically examine the var
ious calculations indicating that the screening of the optical fields
due to electron-electron interaction may reduce the optical susceptibi
lities of these molecules by a large factor and suggest experiments th
at may clarify the issue.