Oxidative stress and neuroinflammation cause many neurological disorders. Recently, it has been reported that molecular hydrogen (H2) functions as an antioxidant and anti-inflammatory agent. The routes of H2 administration in animal model and human clinical studies are roughly classified into three types, inhalation of H2 gas, drinking H2-dissolved water, and injection of H2-dissolved saline. This review discusses some of the remarkable progress that has been made in the research of H2 use for neurological disorders, such as cerebrovascular diseases, neurodegenerative disorders, and neonatal brain disorders. Although most neurological disorders are currently incurable, these studies suggest the clinical potential of H2 administration for their prevention, treatment, and mitigation. Several of the potential effectors of H2 will also be discussed, including cell signaling molecules and hormones that are responsible for preventing oxidative stress and inflammation. Nevertheless, further investigation will be required to determine the direct target molecule of H2.