Abstract: To address the challenges of global climate change, China has proposed the “dual carbon” strategic goal of "carbon peaking and neutrality". Deep underground engineering, including deep underground energy exploitation, geological carbon dioxide sequestration, deep underground energy storage, and the reuse of abandoned mines, provides important techniques for achieving the “dual carbon” goal. Knowledge about the friction-permeability coupling evolution of fractures and faults, both of which are referred to as rock mass discontinuities in this manuscript, is of great significance for the safety and efficiency of deep underground engineering. Here, we present a state-of-the-art review on the coupling mechanisms and control techniques of the friction-permeability coupling of rock mass discontinuities. First, we briefly introduce the key roles of rock mass discontinuities in contemporary deep underground engineering. Second, basic theories related to the friction and permeability of rock mass discontinuities as well as their coupling mechanisms are systematically presented. Finally, we analyze the main mechanisms of seismicity occurrence induced by fluid injection and extraction, and elaborate on the mechanisms and challenges associated with the enhancement of reservoir permeability in deep underground energy exploitation and the leakage in deep underground fluid storage, alongside current control techniques. Based on recent progress, we propose several important issues to be investigated: the effects of clay on the friction-permeability coupling in rock mass discontinuities, the friction-permeability coupling in rock mass discontinuities under constant normal stiffness conditions, the stick-splitting mechanism of hydraulic fractures, etc. Additionally, multi-stage hydraulic fracturing, machine learning, and distributed optical fiber sensing may provide more efficient and intelligent solutions for predicting and controlling the reservoir permeability enhancement in deep underground energy exploitation, leakage risks in deep underground fluid storage, and induced seismic hazards in various deep underground engineering projects.