Energy storage and conversion is a very important link between the steps of energy production and energy consumption. Traditional fossil fuels are natural and unsustainable energy storage medium with limited reserves and notorious pollution problems, therefore demanding for a better choice to store and utilize the green and renewable energies in the future. Unitized regenerative fuel cell (URFC), a compact version of regenerative fuel cell with only one electrochemical cell, is one of the competent technologies for this purpose. A URFC can produce hydrogen fuel through an electrolysis mode to store the excess energy, and output power in a fuel cell mode to meet different consumption requirements. Such a reversible system possesses several distinctive advantages such as high specific energy, pollution-free, and most importantly, the decoupled energy storage capacity with rated power. Based on the different electrolytes utilized, current available URFC technologies include the most common proton exchange membrane (PEM)-based URFC, and other types of URFC such as the alkaline, solid oxide and microfluidic URFCs. This part of the URFC review emphasizes on the PEM-based URFC. Specifically, the research progress on both cell components and systematic issues is introduced. Benefiting from its fairly mature technology stage, the PEM-based URFC has already been applied in aerospace and terrestrial areas. However, for large-scale application, their cost and efficiency are still the obstacles when competing with other energy storage technologies. As for the alkaline, solid oxide and microfluidic types of URFC, their research progress is reported independently in part B of this review.