This critical review examines the dynamic operation of proton exchange membrane (PEM) electrolyzers, focusing on their potential to reduce the levelized cost of green hydrogen and improve grid flexibility. The review highlights the complex interactions between various variables affecting the performance, safety, and degradation of PEM electrolyzers during dynamic operation. Key areas of concern include the impact of load fluctuations, partial loading, and on/off cycles on the efficiency, safety, and longevity of these systems. The review also discusses the role of data-driven approaches, such as machine learning, in addressing the challenges posed by dynamic operation. Despite rapid advancements, the literature lacks holistic studies that consider all interconnected variables affecting the levelized cost of green hydrogen. The review identifies several knowledge gaps and future research directions, emphasizing the need for more comprehensive studies to optimize the dynamic operation of PEM electrolyzers.This critical review examines the dynamic operation of proton exchange membrane (PEM) electrolyzers, focusing on their potential to reduce the levelized cost of green hydrogen and improve grid flexibility. The review highlights the complex interactions between various variables affecting the performance, safety, and degradation of PEM electrolyzers during dynamic operation. Key areas of concern include the impact of load fluctuations, partial loading, and on/off cycles on the efficiency, safety, and longevity of these systems. The review also discusses the role of data-driven approaches, such as machine learning, in addressing the challenges posed by dynamic operation. Despite rapid advancements, the literature lacks holistic studies that consider all interconnected variables affecting the levelized cost of green hydrogen. The review identifies several knowledge gaps and future research directions, emphasizing the need for more comprehensive studies to optimize the dynamic operation of PEM electrolyzers.