In hemodialysis, vascular access is a key issue. The preferred access is an arteriovenous fistula on the non-dominant lower arm. If the natural vessels are insufficient for such access, the insertion of a synthetic vascular graft between artery and vein is an option to construct an arteriovenous shunt for punctures. In emergency situations and especially in elderly with narrow and atherosclerotic vessels, a cuffed double-lumen catheter is placed in a larger vein for chronic use. The latter option constitutes a greater risk for infections while arteriovenous fistula and arteriovenous shunt can fail due to stenosis, thrombosis, or infections. This review will recapitulate the vast and interdisciplinary scenario that characterizes hemodialysis vascular access creation and function, since adequate access management must be based on knowledge of the state of the art and on future perspectives. We also discuss recent developments to improve arteriovenous fistula creation and patency, the blood compatibility of arteriovenous shunt, needs to avoid infections, and potential development of tissue engineering applications in hemodialysis vascular access. The ultimate goal is to spread more knowledge in a critical area of medicine that is importantly affecting medical costs of renal replacement therapies and patients’ quality of life.