In this article previous and recent results of our nonlinear optical s
tudies of low-dimensional structures are surveyed. Size effect in the
optical second-harmonic generation (SHG) from Ag nanocrystals in islan
d films and CdSe quantum dots in glass matrices as well as thermo- and
DC-electric-field-induced effects in SHG from Si-SiO2 multiple quantu
m wells (MQWs) on Si substrate are studied experimentally and theoreti
cally. Essential (by several orders of magnitude) enhancement of quadr
atic optical response upon decrease in the particle size is observed f
or both Ag nanocrystals and CdSe quantum dots. Regular oscillations in
the second-harmonic intensity measured as functions of temperature an
d applied DC electric field are observed for MQWs. It is shown that th
e size effect for metal nanocrystals can result from the fluctuations
of the particle size breaking the local inversion symmetry. Another me
chanism studied (based on concepts of dynamic chaos) describes the obs
erved size effects for both metal and semiconductor particles. The dep
endence of the second-harmonic intensity on the SiO2 layer thickness i
n MQWs is described with taking into account the retardation of the se
cond-harmonic radiation in MQWs, whereas the thermoinduced effect is i
nterpreted as resulting from the optical interference in the MQWs subs
trate having thickness dependent on temperature (due to the thermal ex
pansion). A possible approach to explaining the observed electroinduce
d effect in MQWs is also discussed.