Neutron absorbing materials are critical for the safe storage of spent nuclear fuel (SNF). These materials must not only possess high neutron absorption capabilities but also demonstrate long-term stability and resistance to corrosion. In this review, we classify the different types of neutron absorbing materials and analyze their advantages and limitations. The primary corrosion mechanisms are summarized, including the micro-galvanic effects induced by secondary phases and Cr-depleted regions, and the irradiation-accelerated corrosion caused by SNF irradiation. Additionally, we also discuss the influence of H₃BO₃ and temperature on the corrosion behavior of neutron absorbing materials. Recent scientific studies to alleviate corrosion effects are highlighted, including ameliorating Cr-depleted regions, mitigating surface defects, optimizing interface structures, introducing crystalline defects, increasing alloy chemical complexity and adding corrosion inhibitors. This review aims to provide valuable insights and methodologies for enhancing the corrosion resistance of neutron absorbing materials, thereby supporting the safe storage of SNF.