On the basis of the analysis of published data and in the course of the authors' long-term geochemical and acoustic surveys performed in 1995-2011 on the East Siberian shelf (ESS) and aimed to research the role of the Arctic shelf in the processes of massive methane outbursts into the Earth's atmosphere, some crucially new results were obtained. A number of hypotheses were proposed concerning the qualitative and quantitative characterization of the scale of this phenomenon. The ESS is a powerful supplier of methane to the atmosphere owing to the continued degradation of the submarine permafrost, which causes the destruction of gas hydrates. The emission of methane in several areas of the ESS is massive to the extent that growth in the methane concentrations in the atmosphere to values capable of causing a considerable and even catastrophic warning on the Earth is possible. The seismic data were compared to those of the drilling from ice performed first by the authors in 2011 in the southeastern part of the Laptev Sea to a depth of 65 m from the ice surface. This made it possible to reveal some new factors explaining the observed massive methane bursts out of the bottom sediments.