In power distribution networks, impedance short-circuit faults are hard to detect in their incipient stage, as the fault currents may not be large enough to trip circuit breakers. In this paper, we summarize our research activities in short-circuit fault localization in underground power distribution networks. First, a simulation testbed was built. It can emulate power distribution networks with both bolted and impedance faults. Different impedances can be added to different branches. Power injection points, load nodes, and short-circuit fault locations can all be adjusted by users. Second, a hardware testbed corresponding to the simulation testbed was fabricated. Third, two novel fault localization algorithms (fault signature matching and sparisity recovery) were implemented. Results obtained from the simulation and hardware testbeds have excellent agreement. Our fault localization algorithms are validated by extensive numerical and experimental data. It is observed that, standard voltage measurements at a small number of pre-selected nodes are sufficient to localize the faults precisely; and hence, our fault localization scheme is of low cost. In addition, since our algorithms require only simple matrix calculations, localization within a few cycles (< 50ms) is achievable.