Stenosis is a major cause of failure of hemodialysis vascular grafts and is primarily caused by neointimal hyperplasia (NH) at the anastomoses. The objective of this article is to provide a scientific review of the biology underlying this disorder and a critical review of the state-of-the-art investigational preventive strategies in order to stimulate further research in this exciting area. The histology of the NH shows myofibroblasts (that are probably derived from adventitial fibroblasts), extracellular matrices, pro-inflammatory cells including foreign-body giant cells, a variety of growth factors and cytokines, and neovasculature. The contributing factors of the pathogenesis of NH include surgical trauma, bioincompatibility of the synthetic graft, and the various mechanical stresses that result from luminal hypertension and compliance mismatch between the vessel wall and graft. These mechanical stimuli are focal in nature and may have a significant influence on the preferential localization of the NH. Novel mechanical graft designs and local drug delivery strategies show promise in animal models in preventing graft NH development. Successful prevention of graft stenosis would provide a superior alternative to the native fistula as hemodialysis vascular access.