In recent years, freeform three-dimensional (3D) printing has led to significant advances in the fabrication of artificial tissues with vascularized structures. This technique utilizes a supporting matrix that holds the extruded printing ink and ensures shape maintenance of the printed 3D constructs within the prescribed spatial precision. Since the printing nozzle can be translated omnidirectionally within the supporting matrix, freeform 3D printing is potentially applicable for the fabrication of complex 3D objects, incorporating curved, and irregular shaped vascular networks. To optimize freeform 3D printing quality and performance, the rheological properties of the printing ink and supporting matrix, and the material matching between them are of paramount importance. In this review, we shall compare conventional 3D printing and freeform 3D printing technologies for the fabrication of vascular constructs, and critically discuss their working principles and their advantages and disadvantages. We also provide the detailed material information of emerging printing inks and supporting matrices in recent freeform 3D printing studies. The accompanying challenges are further discussed, aiming to guide freeform 3D printing by the effective design and selection of the most appropriate materials/processes for the development of full-scale functional vascularized artificial tissues.