It is of great value to develop reliable in vitro models for cell biology and toxicology. However, ethical issues and the decreasing number of donors restrict the further use of traditional animal models in various fields, including the emerging fields of tissue engineering and regenerative medicine. The huge gap created by the restrictions in animal models has pushed the development of the increasingly recognized three-dimensional (3D) cell culture, which enables cells to closely simulate authentic cellular behaviour such as close cell-to-cell interactions and can achieve higher functionality. Furthermore, 3D cell culturing is superior to the traditional 2D cell culture, which has obvious limitations and cannot closely mimic the structure and architecture of tissues. In this study, we review several methods used to form 3D multicellular spheroids. The extracellular microenvironment of 3D spheroids plays a role in many aspects of biological sciences, including cell signalling, cell growth, cancer cell generation, and anti-cancer drugs. More recently, they have been explored as basic construction units for tissue and organ engineering. We review this field with a focus on the previous research in different areas using spheroid models, emphasizing aqueous two-phase system (ATPS)-based techniques. Multi-cellular spheroids have great potential in the study of biological systems and can closely mimic the in vivo environment. New technologies to form and analyse spheroids such as the aqueous two-phase system and magnetic levitation are rapidly overcoming the technical limitations of spheroids and expanding their applications in tissue engineering and regenerative medicine.