  A brief non-technical review of the recent study of classical integrable
structures in quantum integrable systems is given. It is explained how to
identify the standard objects of quantum integrable systems (transfer matrices,
Baxter's $Q$-operators, etc) with elements of classical non-linear integrable
difference equations ($\tau$-functions, Baker-Akhiezer functions, etc). The
nested Bethe ansatz equations for $A_{k-1}$-type models emerge as discrete time
equations of motion for zeros of classical $\tau$-functions and Baker-Akhiezer
functions. The connection with discrete time Ruijsenaars-Schneider system of
particles is discussed.
