The increasing gap between clinical demand for tissue or organ transplants and the availability of donated tissue highlights the emerging opportunities for lab-grown or synthetically engineered tissue. While the field of tissue engineering has existed for nearly half a century, its clinical translation remains unrealised, in part, due to a limited ability to engineer sufficient vascular supply into fabricated tissue, which is necessary to enable nutrient and waste exchange, prevent cellular necrosis, and support tissue proliferation. Techniques to develop anatomically relevant, functional vascular networks in vitro have made significant progress in the last decade, however, the challenge now remains as to how best incorporate these throughout dense parenchymal tissue-like structures to address diffusion-limited development and allow for the fabrication of large-scale vascularised tissue. This review explores advances made in the laboratory engineering of vasculature structures and summarises recent attempts to integrate vascular networks together with sophisticated in vitro avascular tissue and organ-like structures. STATEMENT OF SIGNIFICANCE: The ability to grow full scale, functional tissue and organs in vitro is primarily limited by an inability to adequately diffuse oxygen and nutrients throughout developing cellularised structures, which generally results from the absence of perfusable vessel networks. Techniques to engineering both perfusable vascular networks and avascular miniaturised organ-like structures have recently increased in complexity, sophistication, and physiological relevance. However, integrating these two essential elements into a single functioning vascularised tissue structure represents a significant spatial and temporal engineering challenge which is yet to be surmounted. Here, we explore a range of vessel morphogenic phenomena essential for tissue-vascular co-development, as well as evaluate a range of recent noteworthy approaches for generating vascularised tissue products in vitro.