The extent of gas production from shale reservoirs depends heavily on the stress-strain impact on the reservoir. The reservoir's developed stress allows the rocks to fracture naturally. The developed fractures across the reservoir blocks enhance the gas flow from the reservoir towards the wellbore. This review paper provides a comprehensive overview of the technologies and engineering of shale formation permeability behavior and the impact of induced stress and strain. The impacts of stress and strain on the permeability of shale are also studied. This paper presents the effect of stress-strain analysis on gas recovery due to various gas injections, the dependence of gas shale fracture permeability on effective stress and reservoir pressure, analyzing the consequences of various gas injection rates on stress and strain, and the result of stress-strain elongation or variation on hydrocarbon recovery.