Atmospheric escape is one of the key factors controlling the evolution of Mars habitability. This topic has attracted extensive research interests over the past few decades and served as an important scientific object for several Mars missions. In early history, atmospheric escape on Mars was dominated by plasma escape; at present, neutral escape is probably more important. Escaping neutrals include atomic H, He, O, C, and N, the first of which is the lightest species in the Martian upper atmosphere and presumably undergoes easier escape. This study aims to provide a thorough review of the process of atomic H escape on Mars. In the present, such an escape mainly proceeds via thermal evaporation (Jeans escape), which is sensitive to the atomic H density and temperature at the Martian exobase and presents a range of exciting variabilities. Under normal conditions, atomic H is mainly produced via ionospheric chemistry, which drives H 2 dissociation. However, recent investigations have revealed that atomic H escape is substantially enhanced during global dust storms when low-altitude H 2 O can reach high altitude regions via vertical transport, accompanied by the release of H atoms from H 2 O dissociation via ionospheric chemistry. Despite the significant knowledge gained from existing studies, some questions remain to be solved, including (1) how the ideal Jeans formulism could reflect the actual behaviors of H escape on Mars, (2) whether or not the structure of the Martian H corona contains a nonthermal component, and (3) how H escape occurred in early history and how this affected the long-term evolution of the Martian climate.