Successful translation of potential cancer chemotherapeutic drugs to the clinic depends on sufficient predictability of response in the human system through in vitro simulations. High expenditure and longer duration in preclinical and clinical research urge the enhancement of effective in vitro drug screening. 3D models emulate cell morphology, cell–cell and cell–matrix interactions and are physiologically more relevant for predicting drug responses for complex heterogenic cancers, widely replacing conventional cultures. Bioprinting and microfluidic technology facilitate tissue mimetic model construction and multifaceted simulation of physiology, respectively, promising more-appropriate predictability of drug interactions. Precisely, organotypic tissue constructs assembled using cell-laden matrices or organ-on-a-chip serve as realistic tissue models. This review projects the progress toward biomimetic tissue model development, highlighting the emergence of bioprinting and microfluidic technology in in vitro cancer drug screening and pertaining challenges.