The demand for artificial organs has greatly increased because of various aging-associated diseases and the wide need for organ transplants. A recent trend in tissue engineering is the precise reconstruction of tissues by the growth of cells adhering to bioscaffolds, which are three-dimensional (3D) structures that guide tissue and organ formation. Bioscaffolds used to fabricate bionic tissues should be able to not only guide cell growth but also regulate cell behaviors. Common regulation methods include biophysical and biochemical stimulations. Biophysical stimulation cues include matrix hardness, external stress and strain, surface topology, and electromagnetic field and concentration, whereas biochemical stimulation cues include growth factors, proteins, kinases, and magnetic nanoparticles. This review discusses bioink preparation, 3D bioprinting (including extrusion-based, inkjet, and ultraviolet-assisted 3D bioprinting), and regulation of cell behaviors. In particular, it provides an overview of state-of-the-art methods and devices for regulating cell growth and tissue formation and the effects of biophysical and biochemical stimulations on cell behaviors. In addition, the fabrication of bioscaffolds embedded with regulatory modules for biomimetic tissue preparation is explained. Finally, challenges in cell growth regulation and future research directions are presented.