The presence of a vascular access device (or of any intravascular foreign body) inside the bloodstream is often associated with the formation of a connective tissue sleeve around the catheter (often named—erroneously—“fibrin sleeve”). Such sleeve is usually a physiological phenomenon with little or no clinical relevance, but its pathogenesis is still unclear, so that it is frequently confused with venous thrombosis; also, its relationship with other major catheter-related complications, such as venous thrombosis and bloodstream infection, is uncertain. This narrative review tries to convey in a systematic form the current knowledge about pathogenesis, incidence, clinical manifestations, diagnosis, and management of this phenomenon.