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Complex electromagnetic structures have been the subject of numerous studies by scientists and engineers worldwide over the last 150 years since James Clerk Maxwell postulated his now famous namesake equations in 1865. Physicists, electrical engineers, and material scientists have pondered whether one can use inclusions of various geometrical shapes, compositions, alignments, periodicity, and arrangements, distributed within a host dielectric medium, in order to alter and shape the scattering response of the medium due to an impinging incident electromagnetic wave, and as a result design materials with novel, and sometimes exotic, functionalities not found in natural materials, including those in the periodic table. In particular, Victor G. Veselago first theorized in 1967 electrodynamics of materials with Negative Permittivity and Negative Permeability, i.e., the so-called Negative Refractive Index (NRI) or Double-Negative (DNG) metamaterial. Since the 1980s many research groups worldwide have worked on both theory and applications of not only DNG but complex EM structures in general. The works of Nader Engheta stand out in depth, novelty, diversity, and scientific impact among his peers. Engheta started his work on EM materials in 1982 (his first paper on chiral media) and has since made transformative contributions and significant innovations to the theory, experimental verifications, and novel applications of complex electromagnetic structures. He is known as the father of four areas in metamaterials and complex electromagnetic structures: (i) Plasmonic cloaking , which has possible applications in cloaking sensors and antennas, reduction of co-site interference, and RCS reduction of objects. (ii) Near-zero-index metamaterials , with possible applications in supercoupling between guiding structures in both visible and invisible electromagnetic spectrum, as well as in photonic doping, flexible photonics, giant optical nonlinearity, directive thermal emission, and zero-index quantum optics. (iii) Optical lumped nanocircuits ("optical metatronics"), which has possible applications in optical processors at nanoscale, modularized photonics, wireless at nanoscale, analog computing nanomachines, and one-atom-thick optical devices. (iv) Analog computing with materials , with possible applications in information processing at nanoscale, matrix inversion with waves, analog image parallel processing, inverse scattering solvers, and parallel computing. [ABSTRACT FROM AUTHOR]