The electrical power cable is one of the basic energy carriers for electrical transmission in power grids, whose reliability has noticeable impacts on the safety of a power grid. The diagnostic testing contains the diagnostic and locating of the existing fault of electrical power cables, as well as the monitoring the electrical cable state to find the existing and potential faults during their operation, which are both very important for improving the reliability of the power grids. In this paper, we summarize basic mechanisms of the edging and fault of the electrical power cable and review all kinds of known techniques for electrical power cable diagnostic testing. Based on the presented discussion and recent developments of the smart grids, the future challenges of the electrical power cable diagnostic testing are predicted.