In broadband antenna applications, the antenna's cavity is usually loaded with absorbers to eliminate the backward radiation, but in doing so the radiation efficiency of the antenna is decreased. To enhance the radiation efficiency of the antennas EBG structures are used, but they operate over a narrow band. Uniform electromagnetic band gap (EBG) structures are usually periodic structures consisting of metal patches that are separated by small gaps and vias that connect the patches to the ground plane. The electrical equivalent circuit consists of a resonant tank circuit, whose capacitance is represented by the gap between the patches and inductance represented by the via. EBG structures are equivalent to a magnetic surface at the frequency of resonance and thus have very high surface impedance; this makes the EBG structures useful when mounting an antenna close to conducting ground plane, provided the antenna's currents are parallel to the EBG structure. Because EBG structures are known to operate over a very narrow band, they are not useful when used with a broadband antenna. Mushroom-like uniform EBG structures (that use vias) are compact in size have low loss, can be integrated into an antenna to minimize coupling effects of ground planes and increase radiation efficiency of the antenna. The bandwidth of an EBG structure is defined as the band where the reflection-phase from the structure is between +900 to -900. In this dissertation analysis of EBG structures is established using circuit analysis and transmission line analysis. Methods of increasing the bandwidth of EBG structures are explored, by cascading uniform EBG structures of different sizes progressively and vertically (stacked), and applications with different types of antennas are presented. Analyses in this dissertation are compared with previously published results and with simulated results using 3D electromagnetic tools. Validation of applications with antennas is carried by manufacturing prototypes and comparing measured performance with analysis and 3D electromagnetic simulations. The improvements in performance by using wideband progressive EBG and wideband stacked EBG structures are noted.