Mass transfer is a limiting factor when maintaining large tissue constructs in vitro. Once implanted, because of diffusion constraints, only cells located within 100–200 μm of the nearest capillary will receive the necessary nutrients. Therefore, tissue engineering and regenerative medicine (TERM) products intended for vascularized tissues should be vascularized prior to implantation or incorporate in their composition materials and factors that promote rapid vascularization upon implantation. Similarly, sensing of stimuli is of paramount importance for successful tissue regeneration. This chapter highlights the significance of both vascularization and innervation of TERM constructs and models. The different strategies used to achieve vascularized and innervated TERM materials are discussed. Our body also contains avascular tissues like cornea or cartilage, which are briefly discussed too. An overview on the anatomy and physiology of blood vessels, vascularization, nerves, and innervation is also presented to understand the complexity of incorporating nerves and blood vessels into term strategies. This chapter ends with conclusions and questions to strengthen the acquired knowledge.