With the global transition to a sustainable low-carbon economy, methane production and capture technologies are two of the main low-carbon energy technologies, and the reduction of greenhouse gas emissions and the efficient use of energy gases are the main challenges for both technologies. This paper reviews various ways of methane production and storage, such as electrolysis and methanation in production technology, treatment of organic waste water for methane production, microbial electrolysis, and anaerobic digestion of plants. Geological storage, surface tank storage and sorbent material storage are among the storage technologies. The results show that methane production at this stage exists mostly in the laboratory stage and there are few technologies that can support industrial methane production, electrolysis of methane and methanation still cannot be used in industrial production on a large scale due to cost, and anaerobic consumption of fauna has immature technology. In terms of methane storage, more reliance is still placed on surface tanks, and research on geological storage is still limited by the cost and volume per unit storage capacity and sorbent materials that are still in the exploratory stage. Geological storage, for example, is limited to seasonal and cyclical variations and does not allow for efficient long-term storage. In this paper, we have searched through a large body of literature in order to find better solutions to produce and store methane, and hopefully find technologies that are less harmful to the environment as they evolve.