Through the interaction of electromagnetic wave with artificially engineered materials, atypical and exotic electromagnetic behavior can be exhibited that is not prevalent in nature. These synthetic structures are called Metamaterials (Mtms), the Greek prefix ‘meta’ meaning beyond, which can be designed with man-made inclusions and has the technological potential to fill critical voids that exist in the electromagnetic spectrum today. Along those lines, in this thesis I build on the perspective that the broader class of Mtms consists of material systems whose electromagnetic properties have been modified by either: (1) altering the intrinsic properties of a bulk material through the introduction of either volumetric subwavelength structures, or (2) hybrid materials that consist of a host material in association with subwavelength inclusions, such as conducting or dielectric objects. In that context, Left-hand Materials (LHMs), Photonic Band Gap (PBG) and Electronic Band Gap (EBG) materials represent subsets of a more general class of Mtm structures whose electromagnetic properties have been modified, or engineered, for a given application. In more detail, in this thesis I present the application of numerical tools such as the three-dimensional Finite Difference Time Domain (FDTD) method that were developed to characterize the LHMs, artificial composites of split ring resonators (SRRs) and wire structures, in terms of their dispersion diagrams. The highlight of this work was the demonstration of the flow of group and phase velocities in opposite direction. Key to successfully developing this technique was the use of the Pade approximation to interpolate the spectral response of the SRR and reduce the required number of time iterations in the analysis. Following that, a one dimensional FDTD method was incorporated with Drude form to model generic LHM slabs to demonstrate feasibility of low-loss LHM structures through free-space impedance matching network. Along the lines of experimental characterization of Mtms, negative refraction using fabricated LHMs is presented where the negative index of a LHM flat slab was calculated using Snell’s law. Some of the unique applications of Mtms in the microwave frequency regime are investigated wherein miniaturization of narrowband and wideband resonating antennas was demonstrated using artificial inductive materials based on SRRs. This unique approach not only opened up the potential for physical size reduction of the antenna but elucidated the enhancement of the bandwidth of the antenna. Electromagnetic response from Mtm structures can be further enhanced by introducing electrical tunability feature. With regards to that, I present phase modulation based on reconfigurable Mtms. Numerical results of the two designs considered promised a high degree of phase modulation with very minimal transmission loss. This work was further verified with experimental measurements wherein modulation was demonstrated with two different measurement setups that ensured consistency of the data. The numerical and experimental analysis, along with the novel applications based on Mtms presented in this thesis, have the potential to create the platform for the next generation of advanced electromagnetic application and devices.