Vascular access is the lifeline for patients on hemodialysis. Arteriovenous fistulas (AVFs) are the preferred vascular access, but AVF maturation failure remains a significant clinical problem. Currently, there are no effective therapies available to prevent or treat AVF maturation failure. AVF maturation failure frequently results from venous stenosis at the AVF anastomosis, which is secondary to poor outward vascular remodeling and excessive venous intimal hyperplasia that narrows the AVF lumen. Arteriovenous grafts (AVGs) are the next preferred vascular access when an AVF creation is not possible. AVG failure is primarily the result of venous stenosis at the vein-graft anastomosis, which originates from intimal hyperplasia development. Although there has been advancement in our knowledge of the pathophysiology of AVF maturation and AVG failure, this has not translated into effective therapies for these two important clinical problems. Further work will be required to dissect out the mechanisms of AVF maturation failure and AVG failure to develop more specific therapies. This review highlights the major recent advancements in AVF and AVG biology, reviews major clinical trials, and discusses new areas for future research.