The underwater electrical wire explosion (UEWE) is an appealing source of underwater shock waves (SWs) with a high conversion efficiency from electrical energy to mechanical energy, good repeatability and controllability. Industrial applications are already seen in oil-well unblocking and stratum stimulation, and research is currently underway to apply UEWEs in electro-hydraulic forming, exploitation of unconventional gas and oil resources, etc. The emerging new applications call for a review on UEWE research from the perspective of an efficient SW source. This review paper considers the physical processes and numerical simulation methods, electrical and SW characteristics, and current and potential applications, and provides suggestions for future research directions. The code (XJ_UEWE01) developed by the authors to solve a coupling model of UEWE is included. The paper will provide students and researchers new to this field with an explanation of basic concepts of UEWE and a detailed overview of previous studies, and will aid research on UEWE applications, especially device development and parameter optimization.