This paper summarizes current understanding of the processes that determine the dynamics of the subsea permafrost-hydrate system existing in the largest, shallowest shelf in the Arctic Ocean; the East Siberian Arctic Shelf (ESAS). We review key environmental factors and mechanisms that determine formation, current dynamics, and thermal state of subsea permafrost, mechanisms of its destabilization, and rates of its thawing; a full section of this paper is devoted to this topic. Another important question regards the possible existence of permafrost-related hydrates at shallow ground depth and in the shallow shelf environment. We review the history of and earlier insights about the topic followed by an extensive review of experimental work to establish the physics of shallow Arctic hydrates. We also provide a principal (simplified) scheme explaining the normal and altered dynamics of the permafrost-hydrate system as glacial-interglacial climate epochs alternate. We also review specific features of methane releases determined by the current state of the subsea-permafrost system and possible future dynamics. This review presents methane results obtained in the ESAS during two periods: 1994-2000 and 2003-2017. A final section is devoted to discussing future work that is required to achieve an improved understanding of the subject.Significant reserves of CH 4 are held in the Arctic seabed [10], but the release of CH 4 to the overlying ocean and, subsequently, to the atmosphere has been believed to be restricted by impermeable subsea permafrost, which has sealed the upper sediment layers for thousands of years [11]. In the regions where permafrost exists, hydrate-bearing sediment deposits can reach a thickness of 400 to 800 m [12,13]. Shallow hydrate deposits are predicted to occupy~57% (1.25 × 10 6 km 2 ) of the East Siberian Arctic Shelf (ESAS) seabed [14]. It has been suggested that destabilization of shelf Arctic hydrates could lead to large-scale enhancement of aqueous CH 4 , but this process was hypothesized to be negligible on a decadal-century time scale [15].Consequently, the continental shelf of the Arctic Ocean (AO) has not been considered as a possible source of CH 4 to the atmosphere until very recently [16][17][18].The key area of the AO for atmospheric venting of CH 4 is the East Siberian Arctic Shelf (ESAS). The ESAS covers greater than two million square kilometers (equal to the areas of Germany, France, Great Britain, Italy, and Japan combined). This vast yet shallow region has recently been shown to be a significant modern source of atmospheric CH 4 , contributing annually no less than terrestrial Arctic ecosystems [19,20]; but unlike terrestrial ecosystems, the ESAS emits CH 4 year-round due to its partial openness during the winter when terrestrial ecosystems are dormant [21]. Emissions are determined by and dependent on the current thermal state of the subsea permafrost and environmental factors controlling permafrost dynamics [21,22]. Releases could potentially increase by 3-5 orders of magnitude,...