Human in vitro tissues are extracorporeal 3D cultures of human cells embedded in biomaterials, commonly hydrogels, which recapitulate the heterogeneous, multiscale, and architectural environment of the human body. Contemporary strategies used in 3D tissue and organ engineering integrate the use of automated digital manufacturing methods, such as 3D printing, bioprinting, and biofabrication. Human tissues and organs, and their intra‐ and interphysiological interplay, are particularly intricate. For this reason, attentiveness is rising to intersect materials science, medicine, and biology with arts and informatics. This report presents advances in computational modeling of bioink polymerization and its compatibility with bioprinting, the use of digital design and fabrication in the development of fluidic culture devices, and the employment of generative algorithms for modeling the natural and biological augmentation of in vitro tissues. As a future direction, the use of serially linked in vitro tissues as human body‐mimicking systems and their application in drug pharmacokinetics and metabolism, disease modeling, and diagnostics are discussed.