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Proton Exchange Membrane (PEM) water electrolysers have gained attention as efficient and sustainable hydrogen production devices. Understanding their electrical behavior is crucial for optimizing their performance and control strategies. This comprehensive review analyzes both the static and dynamic electrical models, emphasizing the often-neglected dynamic models. Static models reveal steady-state behavior, offering insights into voltage-current characteristics, polarization phenomena, and overall efficiency. On the other hand, dynamic models capture transient responses, enabling an analysis of time-dependent performance and system reactions to input variations, such as flow rate, temperature, pressure, and electrical potential. The review also addresses overlooked diffusion phenomena, crucial for accurate mass transport dynamics and enhancing dynamic model accuracy. Furthermore, the article highlights challenges and research possibilities in electrical modeling, offering insight into future research subjects.