A number of issues associated with the generation and applications of localized waves are addressed in this thesis. First, the salient characteristic features of two canonical localized wave solutions to the scalar wave equation are discussed. Second, novel azimuthally polarized focus wave mode-type and X wave-type localized electromagnetic fields are derived using a vector-valued spectral approach. Third, all reported experiments dealing with the generation of localized waves are discussed and a concise report on field depth measurements, together with practical implications, is presented. Fourth, new methods for generating X waves in the microwave frequency regime are proposed. Emphasis is placed on increasing the field depth. The proposed new feed scheme increases the field depth as much as 10 times compared to the experimental results reported by Mugnai et al. [2000]. Two modified reflector systems are introduced for the generation of X waves. The first uses an offset launcher reflector configuration. The second uses a Cassagrain reflector system with an integrated circular slit. Finally, future work on electromagnetic X wave generation by means of independently addressable array elements is discussed. / Master of Science