In this article, we discuss an approach to the understanding of UV and CD spectra for molecular aggregates and biopolymers. For this aim, sections II and III are intended to provide an elementary introduction. In section III, the Fano-DeVoe approximation is classically introduced. In section II, we describe, rather in detail, particularly the Kramers-Kronig transform of the imaginary part of the polarizability approximated by the Gaussian band shape function. In so doing, the real part of polarizability is represented by a Dawson integral for which, however, we could not find any detailed references as presented here. In section IV, using a monomer`s Gaussian polarizability which is essential for describing the J-bands, we discuss qualitatively the J-bands of pseudoisocyanines in terms of the usual Fano-DeVoe approximation. In sections V and VI, the polarizability theories are outlined in the usual and extended Fano-DeVoe approximations. In section VII, we show how the polymer CD band shape function classically derived by DeVoe can quantum-mechanically be re-derived from the description of optical activity given in the well-known textbook written by Eyring et al. In section VIII, in order to demonstrate that the familiar exciton schematic dimer model of Kasha and coworkers can be confirmed again in terms of our band shape analyses which reproduce their energy-level diagrams, UV spectra for three types of hypothetical chlorophyll a dimers are computed by the Fano-DeVoe polarizability approximation; the three typical dimers have respectively a parallel stacked array, a linear head-to-tail coplanar array, and an obliquely card-packed array. Especially, for obliquely card-packed dimers with skewed, non- eclipsed arrangements of monomers, in which the transition dipoles are skewed in the sense of either a right- or left-handed helix, we mention that computed CD spectra can determine the absolute sense of twist between chromophores. In sections IX and X, applications of the polarizability theories to DNAs and polypeptides are mentioned.