A multitude of recent work predicts many novel concepts based on the availability of non-natural materials; some prominent examples include transformation optics (TO) and perfect lens. The interest in this eld has grown dramatically due to spec- ulated possibility to allow for continuously varying material properties to steer the incident wave at will, such as for the TO. The posed challenges for their realisation include the limitations of numerical modelling and manufacturing techniques. A de- sign scheme has been proposed, in this thesis, for composite materials: the desired electromagnetic properties of composites can be engineered by judiciously varying the volume fraction of the inclusion-to-host materials, by manipulating the geomet- ric arrangement of inclusions, or by altering their dielectric contrast. The analysis of the homogenised response of the designed materials at macro-scale requires effective medium modelling techniques. The existing effective medium approximation tech- niques have been discussed, and their pros and cons outlined. A homogenization scheme has been introduced that is based on the interaction of the incident wave and the nanoparticles at the micro-scale, which further requires efficient electromagnetic modelling. The conventional nanoparticle modelling techniques, as well as the state of the art, have been reviewed and a dipole-moment-based method to efficiently solve modern nanoparticle-based electromagnetic problems has been outlined. The appli- cability of the proposed scheme has been demonstrated by employing it to design various EM devices. An improved permittivity extraction scheme has been proposed for the homogenization of composites. Unlike classical homogenization schemes, the extracted parameters, using the proposed technique, follow the relation between the real and imaginary parts, that is, Kramers-Kronig relations. Several random and periodic structures have been simulated for the purpose of extracting the ef- fective electromagnetic properties and interpreting the results so as to establish a connection between them.