Polymer electrolyte membrane water electrolysis (PEMWE) has been regarded as a promising technology for renewable hydrogen production. However, acidic oxygen evolution reaction (OER) catalysts with long-term stability imposes a grand challenge in its large-scale industrialization. In this review, critical factors that may lead to catalyst's instability in couple with potential solutions are comprehensively discussed, including mechanical peeling, substrate corrosion, active-site over-oxidation/dissolution, reconstruction, oxide crystal structure collapse through the lattice oxygen-participated reaction pathway, etc. Last but not least, personal prospects are provided in terms of rigorous stability evaluation criteria, in situ/operando characterizations, economic feasibility and practical electrolyzer consideration, highlighting the ternary relationship of structure evolution, industrial-relevant activity and stability to serve as a roadmap towards the ultimate application of PEMWE.