This topical review discusses the properties of bioink, the material used in bioprinting, before, during, and after gelation. Bioink, typically a cytocompatible hydrogel precursor, is essential for achieving desired structural resolution, shape fidelity, and cell survival in bioprinted tissue constructs. The review highlights the influence of cell density, proliferation, migration, and interaction with the hydrogel on tissue development and maturation. Numerical models are reviewed and implemented to predict tissue development and optimize bioprinting parameters such as material, cell loading, and construct geometry. The paper also covers various bioprinting methodologies, including inkjet, orifice-free, and extrusion bioprinting, detailing their unique challenges and advantages. Additionally, it explores methods for hydrogel gelation, commercialization of bioprinting devices and materials, and the cytocompatibility of different hydrogels. The effect of cell content on material processing and the prediction of properties of hydrogels containing living cells are also discussed. The review concludes with future perspectives on the development of computational tools to predict and optimize bioprinted constructs, emphasizing the importance of considering cell density and distribution in designing bioprinted structures.This topical review discusses the properties of bioink, the material used in bioprinting, before, during, and after gelation. Bioink, typically a cytocompatible hydrogel precursor, is essential for achieving desired structural resolution, shape fidelity, and cell survival in bioprinted tissue constructs. The review highlights the influence of cell density, proliferation, migration, and interaction with the hydrogel on tissue development and maturation. Numerical models are reviewed and implemented to predict tissue development and optimize bioprinting parameters such as material, cell loading, and construct geometry. The paper also covers various bioprinting methodologies, including inkjet, orifice-free, and extrusion bioprinting, detailing their unique challenges and advantages. Additionally, it explores methods for hydrogel gelation, commercialization of bioprinting devices and materials, and the cytocompatibility of different hydrogels. The effect of cell content on material processing and the prediction of properties of hydrogels containing living cells are also discussed. The review concludes with future perspectives on the development of computational tools to predict and optimize bioprinted constructs, emphasizing the importance of considering cell density and distribution in designing bioprinted structures.