Water electrolysis provides efficient and cost-effective production of hydrogen from renewable energy. Currently, the oxidation half-cell reaction relies on noble-metal catalysts, impeding widespread application. In order to adopt water electrolyzers as the main hydrogen production systems, it is critical to develop inexpensive and earth-abundant catalysts. This review discusses the proton exchange membrane (PEM) water electrolysis (WE) and the progress in replacing the noble-metal catalysts with earth-abundant ones. Researchers within this field are aiming to improve the efficiency and stability of earth-abundant catalysts (EACs), as well as to discover new ones. The latter is particularly important for the oxygen evolution reaction (OER) under acidic media, where the only stable and efficient catalysts are noble-metal oxides, such as IrO_x and RuO_x. On the other hand, there is significant progress on EACs for the hydrogen evolution reaction (HER) in acidic conditions, but how many of these EACs have been used in PEM WEs and tested under realistic conditions? What is the current status on the development of EACs for the OER? These are the two main questions this review addresses.