The article focuses on fundamental aspects of hydrogen electroadsorption on and electroabsorption into metallic electrodes. It emphasises the basic different between hydrogen electroadsorption under electrochemical conditions and hydrogen chemisorption as well as physisorption in low-pressure gas-phase milieu. The respective environments are presented and their characteristics discussed. Under electrochemical conditions, two distinct electroadsorbed H species can be formed depending on the nature of the metallic electrode and the applied potential. Spectroscopic as well as thermodynamic evidence of their existence is presented. The paper elaborates on various electrochemical adsorption isotherms which may be applied to elucidation of thermodynamic state functions of the under-potential deposition of hydrogen. Subsequently, energetics of the process on noble-metal electrodes are presented and results for polycrystalline and single-crystal surfaces of noble-metal electrodes are discussed in detail. The adsorption sites of the under-potential deposited and the over-potential deposited hydrogen are proposed based on the spectroscopic and thermodynamic data. The paper defines the Gibbs energy of the adsorbed, subsurface, and chemisorbed hydrogen, and discusses the gradient of the Gibbs energy associated with the hydrogen interfacial transfer from the electroadsorbed to the absorbed state. Because under electrochemical conditions two electroadsorbed hydrogen species can be formed and because they reveal different physico-chemical properties, it is apparent that they must possess distinct pathways of interfacial transfer. These different electroabsorption pathways are presented and their applicability discussed with regard to the nature of the metallic host. The paper elaborates on the pressure of molecular hydrogen which can build up in the proximity of the electrode surface in terms of the externally applied potential and the system design. It deliberates on the role of certain chemisorbed species, so-called site blocking species, in hydrogen interfacial transfer by acting either as surface promoters or as surface poisons. Thereafter, a section is devoted to the meaning of the volcano relation which relates the exchange current density of the cathodic hydrogen evolution reaction and the metal-hydrogen surface bond energy. In conclusion, the article comments on various aspects of hydrogen electroadsorption and electroabsorption which remains unexplained and proposes new directions of research.