There is an increasing interest in organ-level 3D tissue constructs, owing to their mirroring of in vivo-like features. This has resulted in a wide range of preclinical applications to obtain cell-or tissue-specific responses. Additionally, the development and improvement of sophisticated technologies, such as organoid generation, microfluidics, hydrogel engineering, and 3D printing, have enhanced 3D tissue constructs to become more elaborate. In particular, recent studies have focused on including complex compartments, i.e., vascular and innervation structured 3D tissue constructs, which mimic the nature of the human body in that all tissues/organs are interconnected and physiological phenomena are mediated through vascular and neural systems. Here, the strategies are categorized according to the number of dimensions (0D, 1D, 2D, and 3D) of the starting materials for scaling up, and novel approaches to introduce increased complexity in 3D tissue constructs are highlighted. Recent advances in preclinical applications are also investigated to gain insight into the future direction of 3D tissue construct research. Overcoming the challenges in improving organ-level functional 3D tissue constructs both in vitro and in vivo will ultimately become a life-saving tool in the biomedical field.