In this work, the Finite Difference Time Domain (FDTI)) Method is ernployed to study the characteristics of DR antennas of various configurations, hitherto a difficult task. The advantages of this new type of antenna are its small size, zero conductor loss and flexible feeding configurations, which makes it an ideal candidate for operating at very high frequencies. The FDTD method solves Maxwell's time-dependent curl equations directly in the time domain by converting them into finite-difference equations. These are then solved in a time matching sequence by alternately calculating the electric and magnetic fields in an interlaced spatial grid. The advantage of this approach is the ability to investigate basic structures as well as more elaborate DR antenna structures which are analyzed with difficulty by other previously proposed methods. First, DR antennas excited by axi-symmetrical coaxial probes are investigated. Due to rotational symmetry, the analysis of this type of antenna structure can be treated as a two-dimensional electromagnetic problem. An efficient near-to-far field transformation is developed to compute the far-fields of the antenna. It is demonstrated that the use of annular ring DRs with high εr, is feasible for antenna applications. Bandwidth enhancement techniques for this type of antenna are also considered. Numerical results are validated by measurements. Next, the method is extended to three-dimensional space to analyze general probe-fed cylindrical DR antennas. Numerical results for the input impedance a d radiation patterns of the DR antenna operating in HEM11δ mode are presented, and compare favorably with measurements. The effects of various parameters on the characteristics of the DR antenna are studied. Fabrication imperfection effects and the cross-polarization characteristics of this type of DR antenna are also investigated for the first time. Finally, the rigorous analysis of aperture-coupled cylindrical DR antennas is performed. Aperture coupled excitation has a number of advantages over the probe-fed version such as the ease of integration and the avoidance of large probe self reactance at millimeter frequencies. In contrast to previous theoretical studies, this analysis includes the simulation of a microstrip line circuit feeding the DR antenna. Numerical results for the input impedance and radiation patterns of an aperture-coupled DR antenna operating in HEM11δ mode are presented and confirmed by measurement. The effects of various parameters on the characteristics of the DR antenna are studied. This approach is also applied to optimize the bandwidth of an aperture-coupled stacked cylindrical DR. The computed return loss of the antenna is illustrated and validated by measurements.