Proton exchange membrane (PEM) electrolyzer is an advanced technology considered a viable alternative for the generation of hydrogen-based on renewable energy sources (RES). Its modeling is essential to study its interaction with RES and power electronics. In the current literature, the models for the electrical domain are mainly based on semi-empirical and empirical equations. However, dynamic operations are generally neglected. Besides, a few works about electrolyzer efficiency have been reported, especially Faraday's efficiency, which is a key parameter to express the losses due to gas diffusion. The main purpose of this review is to summarize and analyze the reported models to describe the electrical domain. Furthermore, dynamic operation issues are highlighted and recent works about modeling the dynamics are introduced. Finally, a discussion is provided about the different efficiency (Faraday, voltage, energy) and the specific energy consumption, which are important indicators linked with the performance. (C) 2020 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.