Additive manufacturing encompasses a group of 3D printing technologies enabling the generation of complex, biomimetic 3D structures for tissue engineering and regenerative medi- cine. The ability of 3D printing to pattern multiple materials, cell types and biomolecules provides a unique tool to create tissue constructs closely resembling the composition, architecture and function of biological tissues. Advances in printable bio- materials and 3D printing strategies allow the fabrication of vascularised tissue constructs composed of multiple cells embedded within suitable extracellular matrix components and supplied by functional vasculature. Thick and perfusable vascular tissue constructs can now be designed, printed and in vitro cultured for relevant time periods, offering a promising alternative to traditional vascularisation strategies. This review provides a concise overview of recent 3D printing strategies explored to create vascular networks and vascularised tissue constructs, and discusses future perspectives regarding the importance of engineering vascularisation for clinical applications.