Three-dimensional (3D) printing has rapidly evolved, with major applications in the field of medicine. One of the greatest advances leading to 3D bioprinting was the development of biomaterials, cells and supporting components for the fabrication of functional living tissues. Several different methods and techniques of 3D bioprinting are briefly described in this review article, and applications of 3D printing for the fabrication of artificial blood vessels and grafts are presented. Advances in additive manufacturing techniques, medical imaging modalities, biomaterials and cellular engineering will lead to further developments in the fabrication of patient-specific vascular tissue constructs. Futuremultidisciplinary research and innovations are expected to further transform the fields of tissue engineering and regenerative medicine.