Ab initio results of the electronic structure and conduction properties of both periodic and aperiodic DNA and protein models are reviewed. Band structure results of the periodic systems are obtained on the basis of theab initio Hartree-Fock crystal orbital method. The electronic density of states (DOS) of the multicomponent periodic and aperiodic polypeptide chains, and of single-stranded periodic and aperiodic DNA, on the other hand, are determined using theab initio matrix block negative factor counting technique. Large values of the fundamental energy gap obtained for all the systems studied rule out the possibility of intrinsic conduction in them. The DOS curves of aperiodic DNA and polypeptide chains, in contrast to those of corresponding periodic systems, are found to consist of relatively broader regions of allowed energy states with a few small gaps in between. The study of the localization properties of the lowest unoccupied energy levels in the conduction band region of aperiodic polypeptide chains indicates that these wavefunctions are highly localized. In the light of these results, the possibility of charge transport through hopping conduction in proteins under the assumption of charge transfer to the polypeptide chains is discussed. Finally, how the correlation effects could be considered in an approximate way for these biopolymers is outlined.