Source localization has always been a popular research area in the literature. It refers to the process of determining the unknown position of a particular object. Although numerous approaches have already been developed, they mostly focus on localization in non-dispersive mediums, e.g. air. There is not much literature for the dispersive scenario. In a dispersive medium, the wave propagation speed is frequency dependent. Instead of maintaining the waveform, the signal would spread out as it propagates. This phenomenon highly reduces the accuracy of conventional algorithms that utilize time measurements for estimation. The first part of the thesis is on the development of accurate localization approaches with the frequency dependent velocity assumed to be available. By comparing with the derived performance bound, it has been proved that one of the proposed algorithms is able to provide optimal estimates. A theoretical study on the influence of sensors placement to localization limits has also been performed. It is derived that uniform angular arrays and its superpositions could attain the highest accuracy. Besides that, the situation of unknown dispersion function has also been investigated. By placing the sensors at a known separation, the dispersion curve can be determined experimentally by considering the phase differences between sensors. With the estimated curve, the problem could be simplified to the scenario of known velocity. Finally, an algorithm that can perform localization directly without knowing the velocity is also developed, but its estimate is not optimum.