  I present a review of both experimental and theoretical studies performed
during the recent three years, which deal with the physical properties and
possible applications of graphene placed on ferroelectric (organic or
Pb(ZrxTi1-x)O3 (PZT) ceramic) substrates. The system 'graphene-on-ferroelectric
substrate' has unique advantages in comparison with the graphene deposited on
SiO2 or on dielectrics with high dielectric permittivity. In particular, one
can obtain high (~ 1012 cm-2) carrier concentrations in the doped
graphene-on-ferroelectric structures for moderate (of the order of 1 V) gate
voltages. The existence of a hysteresis (or anti-hysteresis) in the dependence
of electrical resistance of graphene channel on the gate voltage facilitates
creating bistable systems for different applications. The use of ferroelectric
substrates has already enabled developing of robust elements of non-volatile
memory of a new generation. These elements operate for more than 105 switching
cycles and store information for more than 103 s. Such systems can be
characterised theoretically by ultrafast switching rates (~ 10-100 fs). A
theoretical analysis has also demonstrated that the structures 'graphene-on-PZT
ferroelectric substrate' would result in developing efficient and fast
small-sized modulators of mid-IR and near-IR radiations for different
optoelectronic applications.
