Human saphenous vein has long been used as coronary artery bypass grafts to survive a heart arrested by blocked coronary arteries. Biomechanical properties of the saphenous vein can be critical because mismatch in the biomechanical property between a coronary artery and a graft will reduce graft patency and speed up disease development in the graft. In this paper hence the active and passive biomechanical behaviours of the human saphenous vein and other venous walls were reviewed extensively and comprehensively. The existing in vitro uniaxial, bulge, planar and tubular biaxial tensile testing methods, in vivo testing cases, property variables, various tested results, constitutive models and their mathematical modelling methods, viscoelasticity, and residual strain/stress are highlighted and summarized. It is demonstrated that the biomechanical properties of the human saphenous vein and other venous walls are not well documented, and their modelling approaches are limited and subjected to be updated in a great deal. Additionally, a few important research issues are proposed. The paper has provided a piece of useful information to investigation into coronary artery bypass grafts.