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Water-electrolysis is a promising technology for hydrogen production, but the precious metal catalysts (such as Ir and Pt) used in water-electrolysis limit its commercial application at a large scale. In order to further reduce the cost of hydrogen production by water-electrolysis, the development of efficient, stable and low-cost electrocatalysts is the focus of current research. Theoretical calculation is helpful to find out the general principle between catalysts structure, adsorption properties of intermediates and catalytic activity to reduce the research and development cost of novel catalysts. The volcano relationships are widely used in hydrogen evolution reaction(HER) and oxygen evolution reaction(OER) to provide a fundamental theory for high-throughput screening of high-active catalysts. The reaction mechanism of HER and OER is summarized, the basic concept of the volcano relationships of HER and OER is expounded, and the general method constructing the volcano relationships is also summarized. [ABSTRACT FROM AUTHOR]