Vibrational excitation in electron collisions with polyatomic molecule
s is reviewed. Theoretical treatments based on the fixed-nuclear-orien
tation approximation are summarized. Results of the theoretical studie
s of H2O, H2S and CH4 are presented as an example and compared with ex
perimental data. A calculation in the Born approximation with a long-r
ange electrostatic interaction is also shown. In particular, the usefu
lness of the Born approximation with a dipole interaction is examined
in detail. Finally possible further improvement of the theory is discu
ssed.