An electrically small electric dipole antenna is known to be a very inefficient radiator, i.e., because it has a very small radiation resistance while simultaneously having a very large capacitive reactance, a large impedance mismatch to any realistic power source exists. It has been demonstrated recently that enclosing an electrically small electric (magnetic) dipole antenna in an electrically small epsilon-negative (ENG) (mu-negative (MNG)) shell leads to an efficient electrically small radiator. The inductive (capacitive) nature of the ENG (MNG) shell compensates for the capacitive (inductive) nature of the electrically small electric (magnetic) dipole antenna, i.e., it functions as a distributed matching element that forms this "geometrically" resonant system. More realistic electrically small center-fed electric dipole-ENG spherical shell and coax-fed electric monopole-ENG hemispherical shell antenna systems have also been modeled numerically using ANSOFT's High Frequency Structure Simulator (HFSS) and COMSOL's Multiphysics simulator. The input resistance and reactance of these realistic antenna-ENG shell systems have been obtained from these numerical models. It has been shown that these systems could be designed to have geometrical resonances for which the relative gains were analogous to the radiated power ratios obtained with the analytical models. With further tuning, it has also been shown that an "antenna" resonance, where the system has a zero input reactance and an input resistance which is matched to a specified source resistance, can also be realized to yield a very high overall efficiency. The effects of losses and frequency dispersion on these systems have been studied. With dispersion engineering available from the use of active metamaterials, the large bandwidths obtained with the dispersionless metamaterial models can again be obtained even in the presence of losses and dispersion. This suggests the possible realization of metamaterial-based broad bandwidth efficient electrically-small antennas. The predicted high overall efficiencies (> 90%) have been obtained with several recently developed metamaterial-inspired electrically-small antennas: the 2D (planar) and 3D (volumetric) electric-based and magnetic-based EZ antennas. The EZ antenna designs, simulations and experiments will be described. The experimental data are in very good agreement with the simulation results.