The present status of the quantum theory of polymers, with emphasis on
recent developments, is reviewed. After a brief discussion of the Har
tree-Fock crystal orbital method, both in its ab initio and semiempiri
cal forms, to calculate the energy band structure of periodic polymers
, theoretical methods for the treatment of disorders as well as electr
on correlation in both periodic and aperiodic polymers are discussed.
The Green matrix formalism developed for studying the interface betwee
n two quasi-one-dimensional chains is also briefly mentioned. Finally,
some results including a few new ones, obtained using the above theor
etical methods are presented with an aim to demonstrate the capabiliti
es of the contemporary quantum theory of polymers.