The investigation of vascular biometric traits has become increasingly popular during the last years. This book chapter provides a comprehensive discussion of the respective state of the art, covering hand-oriented techniques (finger vein, palm vein, (dorsal) hand vein and wrist vein recognition) as well as eye-oriented techniques (retina and sclera recognition). We discuss commercial sensors and systems, major algorithmic approaches in the recognition toolchain, available datasets, public competitions and open-source software, template protection schemes, presentation attack(s) (detection), sample quality assessment, mobile acquisition and acquisition on the move, and finally eventual disease impact on recognition and template privacy issues.