Dielectric properties of heterogeneous materials for various condensed-matter systems have been gaining world-wide attention over the past 50 or so years in the design (or engineering) of materials structures for desired properties and functional purposes. These applications range from cable and current limiters to sensors. These multiscale systems lead to challenging problems of connecting micro- or meso-structural features to macroscopic materials response, i.e. permittivity, conductivity. This article first reviews progress made at that time of the underlying physics of dielectric heterostructures and points out the missing elements that have led to a resurgence of interest in these and related materials. Recent advances in computational electromagnetics provide unparalleled control over morphology in this class of materials to produce a seemingly unlimited number of exquisitely structured materials endowed with tailored electromagnetic, and other physical properties. In the text to follow, we illustrate how an ab initio computational technique can be used to accurately characterize structure-dielectric property relationships of periodic heterostructures in the quasistatic limit. More specifically, we have carried out two-dimensional (2D) and three-dimensional (3D) numerical studies of two-component materials in which equal-sized inclusions, with shape and orientation and possibly fused together, are fixed in a periodic square (2D) or cubic (3D) array. Boundary-integral equations (BIE) are derived from Green's theorem and are solved for the local field with appropriate periodicity conditions on a unit cell of the structures using the field calculation package PHI3D. A number of illustrative examples shows how this computational technique can provide very accurate predictions for the complex effective permittivity of translationally-invariant heterostructures. The performance of the method is also compared with those of other computational and analytical techniques. We comment on how this computational method helps identify some important characteristics for rationalizing and predicting the structure of composite materials in terms of the nature, size, shape and orientation of their constituents. (C) 2003 Elsevier Science Ltd. All rights reserved.