Soft open points (SOPs) are power electronic devices that are usually placed at normally open points of electricity distribution networks to provide flexible power control to the networks. This paper gives a comprehensive overview of both academic research and industrial practice on SOPs in electricity distribution networks. The topologies of SOPs as multi-functional power electronic devices are identified and compared, which include back-to-back voltage source converters, multi-terminal voltage source converters, unified power flow controllers, and direct AC-to-AC modular multilevel converters. The academic research is reviewed in three aspects, i.e., benefit quantification, control, and optimal siting and sizing of SOPs. The benefit quantification indices are categorized into feeder load balancing, voltage profile improvement, power losses reduction, three-phase balancing and DG hosting capacity enhancement. The control of SOPs is summarized as a three-level control structure, where the system-level and converter-level control are further discussed. For optimal siting and sizing of SOPs, problem formulation and solution methods are analyzed. Besides the academic research, practical industrial projects of SOPs worldwide are also summarized. Finally, opportunities of research and industrial application of SOPs are discussed.