The hierarchical network of blood vessels comprises the larger vessels (veins and arteries), the smaller ones (venules and arterioles), and the thinnest capillaries. The proper functioning of most tissues in the body relies on vascularization, which is meant for the diffusion of gases, nutrients, and harmful waste. However, it is known that cell survival is compromised as the diffusion of oxygen is limited beyond 100–200 µm and damage can occur at any level of the complex system of the vascular network, as is the case in cardiovascular, musculoskeletal, and neurovascular diseases that recur and progress with age. These may prove fatal, hence the need for vascular tissue engineering (VTE) arises. VTE mainly focuses on the fabrication of vascular constructs using natural, synthetic material, or a combination of both using various techniques. The construct is expected to integrate and anastomose with the host vasculature. 4D bioprinting is an emerging field that allows the fabrication of hollow tubes employing different materials that respond to different stimuli. This review is a comprehensive summary of the major techniques employed in VTE and the recent technique of 4D bioprinting foreseen to revolutionize the field. © 2023 The Authors. Advanced Materials Technologies published by Wiley-VCH GmbH.