One-atom-thick material such as graphene, graphene derivatives and graphene-like materials, usually has a dense network lattice structure and therefore dense distribution of electronic clouds in the atomic plane. This unique structure makes it have great significance in both basic research and practical applications. Studies have shown that molecules, atoms and ions are very difficult to permeate through these above-mentioned two-dimensional materials. Theoretical investigations demonstrate that even hydrogen, the smallest in atoms, is expected to take billions of years to penetrate through the dense electronic cloud of graphene. Therefore, it is generally considered that one-atom-thin materialis impermeable for hydrogen. However, recent experimental results have shown that the hydrogen atoms can tunnel through graphene and monolayer hexagonal boron nitride at room temperature. The existence of defects in one-atomthin material can also effectively reduce the barrier height of the hydrogen tunneling through graphene. Controversy exists about whether hydrogen particles such as atoms, ions or hydrogen molecules can tunnel through two-dimensional materials, and it has been one of the popular topics in the fields of two-dimensional materials. In this paper, the recent research progressof hydrogen tunneling through two-dimensional materials is reviewed. The characteristics of hydrogen isotopes tunneling through different two-dimensional materials are introduced. Barrier heights of hydrogen tunneling through different graphene and graphene-like materials are discussed and the difficulties in its transition are compared. Hydrogen cannot tunnel through the monolayer molybdenum disulfide, only a little small number of hydrogen atoms can tunnel hrough graphene and hexagonal boron nitride, while hydrogen is relatively easy to tunnel through silicene and phosphorene. The introduction of atomic defects or some oxygen-containing functional groups into the two-dimensional material is discussed, which can effectively reduce the barrier height of the hydrogen tunneling barrier. By adding the catalyst and adjusting the temperature and humidity of the tunneling environment, the hydrogen tunneling ability can be enhanced and the hydrogen particles tunneling through the two-dimensional material can be realized. Finally, the applications of hydrogen tunneling through two-dimensional materials in ion-separation membranes, fuel cells and hydrogen storage materials are summarized. The potential applications of hydrogen permeable functional thin film materials, lithium ion battery electrode materials and nano-channel ions in low energy transmission are prospected. The exact mechanism of hydrogen tunneling through two-dimensional material is yet to be unravelled. In order to promote these applications and to realize large-scale production and precision machining of these two-dimensional materials, an in-depth understanding of the fundamental questions of the hydrogen tunneling mechanism is needed. Further studies are needed to predict the tunneling process quantitatively and to understand the effects of catalyst and the influences of chemical environments.