In this work, we have undertaken a theoretical approach to the complex problem of modeling the flow of electromagnetic waves in photonic crystals. Our focus to address the feasibility of using the exciting phenomena of photonic gaps (PBG) in actual applications.;We start by providing analytical derivations, as well as the underlying physical principles, of the computational electromagnetic methods used in our work. A comparative study of the strengths and weaknesses of each method is provided. The Plane Wave expansion, Transfer Matrix, and Finite Difference Time Domain Methods are addressed. We also introduce a new theoretical approach, the Modal Expansion Method.;We then shift our attention to actual applications. We begin with a discussion of 2D photonic crystal wave guides. The structure addressed consists of a 2D hexagonal structure of air cylinders in a layered dielectric background. Comparison with the performance of a conventional guide is made, as well as suggestions for enhancing it. Our studies provide an upper theoretical limit on the performance of such guides.;Next, we study 3D metallic PBG materials at near infrared and optical wavelengths. Our main objective is to study the importance of absorption in the metal and the suitability of observing photonic band gaps in such structures. We study simple cubic structures where the metallic scatterers are either cubes or interconnected metallic rods. The effect of topology is also addressed. Our results reveal that the best performance is obtained by choosing metals with a large negative real part of the dielectric function, together with a relatively small imaginary part. Finally, we point out a new direction in photonic crystal research that involves the interplay of metallic-PBG rejection and photonic band edge absorption. We propose that an absolute metallic-PBG may be used to suppress the infrared part of the blackbody emission and, emit its energy only through a sharp absorption band. Potential applications of this new PBG mechanism include highly efficient incandescent lamps and enhanced thermophotovoltaic energy conversion. The suggested lamp would be able to recycle the energy that would otherwise go into the unwanted resulting in a 40% increase in efficiency.