Power line communications (PLC) has attracted considerable attention for supporting smart grid applications. Since it reuses the existing grid infrastructure, it offers cost advantages over alternative communications methods and gives electric utilities control over the communications medium. Furthermore, the "through-the-grid" property of PLC extends its possible use beyond mere communications. Since the PLC signals are bound to travel through the power grid, they can also be used for inference tasks, such as online diagnostics of power line integrity. In this paper, we consider such an inference application of PLC, enabled by modern signal processing. We assume a power grid at whose edges PLC devices are deployed to form a PLC network for purposes such as advanced meter reading. We are interested in retrieving the physical power-grid topology, i.e., the connections and lengths of power lines reaching to the locations of the PLC devices. To this end, we propose the combination of PLC-based ranging with inference based on end-to-end measurements. In the context of communication networks, the latter is known as tomography and hence, we refer to the developed method as power grid tomography. For the purpose of ranging we formulate a new super-resolution ranging algorithm specifically tailored for signal propagation through power lines. Numerical results for low-voltage distribution grid examples demonstrate the successful reconstruction of the grid topology by the proposed power grid tomography method.