Asymptomatic carotid stenosis is a relatively frequent pathology, although when considering the possibility of managing it surgically, there is still an important amount of disagreement concerning the criteria to be taken into account. This study conducts a broad examination of the condition, from its concept and epidemiology to the studies that triggered the boom in its surgical treatment during the nineties. The research also reviews the tools available for a better selection of cases that could potentially benefit most from surgery, the presence of silent brain lesions, the severity of the stenosis, its progression, the characteristics of the plaque, colaterality and vasoreactivity studies, the detection of micro-emboli, the presence of risk factors independently associated to the symptomatic conversion of the stenosis, and other elements that have recently been reported either clinically or experimentally. Finally, the article outlines the current state of the surgical technique and the advances being made in its pharmacological treatment. This review is not intended to be a set of clinical practice guidelines, but to offer a global integrating overview of the management of high-grade asymptomatic carotid stenosis.