Fractures are pervasive in subsurface rock formations and strongly influence fluid migration, heat transport, storage capacity, and mechanical stability. Their hydraulic behavior is central to unconventional hydrocarbon recovery, geothermal development, underground energy storage, and geological carbon dioxide sequestration. However, natural fractures rarely behave as smooth and idealized parallel-plate channels. Surface roughness generates uneven contacts, heterogeneous apertures, and tortuous pathways, making fracture permeability scale-dependent, stress-sensitive, and potentially nonlinear. A unified understanding of how measurable surface geometry controls these responses remains lacking, particularly under coupled thermal and pressure conditions. This review examines how roughness descriptors can be translated into aperture-field structures, flow-control parameters, and cross-scale model inputs. It synthesizes recent advances in interface characterization, roughness-controlled flow mechanisms, coupled thermal and pressure responses, and predictive modeling. Particular attention is given to the transition from two-dimensional empirical indices to three-dimensional statistical, fractal, and self-affine descriptions. The available evidence shows that roughness affects flow mainly through the coupled evolution of contact topology, aperture connectivity, and pathway tortuosity. These processes redistribute local velocities, reorganize preferential channels, promote recirculation, and alter the relationship between pressure gradient and volumetric flow rate. Their hydraulic consequences cannot therefore be represented reliably by mean aperture or a single roughness index alone. Temperature variations and effective stress further modify contact-area distributions and hydraulic apertures through thermally induced deformation and stress-dependent fracture closure. These interactions intensify permeability hysteresis and produce loading-path and thermal-history dependence, complicating parameter transfer between laboratory tests and field-scale predictions. Existing models are consequently evolving from parallel-plate corrections and empirical permeability relations toward structure-informed formulations, discrete-fracture representations, multiscale upscaling, and data–physics integration. However, progress remains limited by inconsistent roughness metrics, insufficient three-dimensional experimental datasets, scale effects, and weak validation under realistic coupled conditions. Future research should establish dimensionally consistent links among surface morphology, contact topology, aperture connectivity, and effective permeability. It should also integrate high-resolution imaging, in situ monitoring, controlled experiments, and uncertainty quantification across representative scales. Physics-informed and graph-based learning may assist parameter inversion and rapid prediction, but their constraints and extrapolation limits require transparent evaluation. By clarifying the geometry-to-structure-to-flow pathway, this review provides a framework for selecting roughness descriptors and constructing transferable fracture-flow models. These advances can improve hydraulic predictions and risk assessment for unconventional hydrocarbon recovery, geothermal development, underground energy storage, and geological carbon dioxide sequestration.