Structural and functional models of [Fe], [FeFe] and [NiFe] hydrogenases using earth abundant metals (Fe and Ni) have been developed for electrocatalytic and photocatalytic hydrogen evolution reaction (HER) in relation to the structure and functions of the hydrogenases. In the X-ray crystal structure of the μ-hydride complex of [NiFe] hydrogenase from Desulfovibrio vulgaris Miyazaki F, the hydride ion is located on the Ni center rather than the Fe center. Thus, mononuclear Ni-hydride complexes act as the most efficient HER catalyst among various metal (Fe, Mn, Cu and Co) hydrides, enabling the reversible interconversion between H2 and H+. A number of X-ray crystal structures of metal-hydride complexes, which are regarded as intermediates for HER, have been clarified. The X-ray crystal structures of polyhydrido copper clusters provide valuable insight into the HER functions of rhombus-shaped Cu nanoparticles (NPs). The detailed catalytic mechanisms of HER via cobalt-hydride complexes are discussed in both thermal and photocatalytic HERs, providing rational design principles for development of more efficient, selective and robust earth-abundant metal catalysts for thermal and photocatalytic HER to replace precious and high cost Pt catalysts.