World energy problems can largely be solved in the event of discovering huge amounts of gaseous hydrogen in a free state, which is considered as a promising alternative to the reserves of traditional fossil fuel in the earth’s crust. However, the hydrogen industry’s development is inhibited by many challenges, in particular, in geology. Today there is neither strategy for exploration activity nor resource evaluation due to the lack of relevant experience and practical recommendations aimed at geological hydrogen. The purpose of the work is to establish and analyze potential ways and geological conditions for the formation, migration, and accumulation of hydrogen of natural origin in the earth’s crust for the further justification of the concept of the search of free hydrogen accumulation. The author has considered all possible theoretical natural sources and ways of generating hydrogen naturally. Its origin is generally assumed to magmatic, thermogenic, endogenous, biogenic, as well as one that is caused by radiolysis, decomposition of organic matter, the interaction of water with reducing agents in the mantle. All known possible ways of the genesis of free hydrogen in natural conditions are analyzed. Geologically controlled sources of natural hydrogen can be grouped according to the main processes: aqueous processes of hydrolysis (several processes including the oxidation of iron minerals, radiolysis, cataclasis and metamorphism; decomposition of organic matter (including thermal maturing); decomposition of hydrogen-containing compounds (in particular, methane and/or ammonia at metamorphisms); deep degassing of Earth’s interior. Potential location areas of free hydrogen in a geological environment are analyzed. Natural conditions for high/increased hydrogen content have basins with the presence of hydrocarbons, recent deposits with prolific organic, coal beds, zones of tectonic faults, extrusive magmatic bodies, alkaline magmatic complexes, geothermal fields, crystalline basements, geologic formation of rocks enriched with potassium, salt-bearing sections and ultrabasic rocks. Due to the uncertainty concerning the ways and conditions for generating hydrogen in the earth’s crust, geological searches and possible further study of hydrogen accumulations require a mix of methods and approaches used for traditional searches of hydrocarbon deposits – conventional oil and gas fields (source rocks, basin, cap) given the features of free hydrogen, in particular, mobility and reactive capacity of its molecule. Regardless of the genesis of hydrogen, the main search criteria should be focused on the ways of its migration and the availability of a basin and a cap. This approach maximally combines hypotheses competing among themselves (from the viewpoint of the genesis of hydrogen). It is required the geological structure with the corresponding basin and fluid trap (cap), which, unlike the fluid traps in the usual sense, should be not only impermeable but also chemically neutral in relation to hydrogen.