In this paper, we review the state of the art in the detection, location, and diagnosis of faults in electrical wiring interconnection systems (EWIS) including in the electric power grid and vehicles and machines. Most electrical test methods rely on measurements of either currents and voltages or on high frequency reflections from impedance discontinuities. Of these high frequency test methods, we review phasor, travelling wave and reflectometry methods. The reflectometry methods summarized include time domain reflectometry (TDR), sequence time domain reflectometry (STDR), spread spectrum time domain reflectometry (SSTDR), orthogonal multi-tone reflectometry (OMTDR), noise domain reflectometry (NDR), chaos time domain reflectometry (CTDR), binary time domain reflectometry (BTDR), frequency domain reflectometry (FDR), multicarrier reflectometry (MCR), and time-frequency domain reflectometry (TFDR). All of these reflectometry methods result in complex data sets (reflectometry signatures) that are the result of reflections in the time/frequency/spatial domains. Automated analysis techniques are needed to detect, locate, and diagnose the fault including genetic algorithm (GA), neural networks (NN), particle swarm optimization, teaching-learning-based optimization, backtracking search optimization, inverse scattering, and iterative approaches. We summarize several of these methods including electromagnetic time-reversal (TR) and the matched-pulse (MP) approach. We also discuss the issue of soft faults (small impedance changes) and methods to augment their signatures, and the challenges of branched networks. We also suggest directions for future research and development.