Fiber-reinforced polymer matrix composites are increasingly considered for lightweight cryogenic pressure vessels due to their excellent combination of tailorability, specific mechanical properties, and relatively low coefficients of thermal expansion. However, significant challenges must be overcome to fully utilize PMCs for cryogenic fuel tanks in terms of transverse microcracking and subsequent permeation of cryogenic fuel. Gas permeation and microcrack densities of cryogenically cycled composites are highly influenced by their layup, ply thickness, load case, and manufacturing defects like voids and resin rich zones. There has been a significant amount of research on measuring gas permeation of composites fatigued under pure thermal or uniaxial thermo-mechanical stresses. However, results demonstrate that the gas permeability should be measured under biaxial thermo-mechanical stresses to properly gauge the leakage characteristics of damaged composites. This paper summarizes the results from over a hundred papers on the key parameters that influence the gas permeability of composites, appropriate testing methods to cycle composites for permeability measurement, methods to limit the evolution of transverse microcracks, and materials traditionally used for the fabrication of all-composite cryogenic fuel tanks. Thin plies and nanofiller-toughening of the matrix have been shown to provide significant improvements in transverse microcrack suppression within cryogenically cycled composites.