The introduction of the so-called metamaterials, artificial materials which have engineered electromagnetic responses that are not readily available in nature, and their exotic properties have provided an alternate design approach that has led to improved performance characteristics of several radiating and scattering systems. This dissertation work introduces an antenna design paradigm based on the incorporation of metamaterials, which have negative permittivity and/or permeability medium properties, with simple radiating elements to obtain efficient electrically-small antenna systems. The most general analytical form of the electrically-small electric dipole antenna in the presence of a multilayered metamaterial shell system is developed and the total radiated power of this system is optimized using a hybrid genetic algorithm(GA)-MATLAB optimization approach. The numerical modeling of more realistic antenna-metamaterial systems confirms the analytical results. The theoretical and numerical studies of their radiation and resonance behaviors have led this dissertation work to the discovery of the first physical two- (2D) and three-dimensional (3D) metamaterial based and inspired efficient electrically-small antenna systems. Several novel metamaterial-inspired electrically-small antenna systems, i.e., the 2D and 3D electrical- and magnetic-based EZ antennas, are reported and are shown to be naturally matched to a 50 Ohms source and, hence, to have high overall efficiencies. The proposed 2D and 3D EZ antenna systems are linearly scalable to a wide range of frequencies. Several versions of the 2D EZ antennas were fabricated and tested. The measurement results confirm the performance predictions. This dissertation also considers several new metamaterial structures. An artificial magnetic conductor (AMC) slab is designed to achieve its in-phase reflection properties in the X-band at 10 GHz without the presenceof a PEC ground plane. A block of this AMC structure was designed, fabricated, tested, and then integrated with a dipole antenna to realize a resonant low profile antenna system having a large front-to-back ratio.