Three-dimensional (3D) bioprinting technologies involving photopolymerizable bioinks (PBs) have attracted enormous attention in recent times owing to their ability to recreate complex structures with high resolution, mechanical stability, and favorable printing conditions that are suited for encapsulating cells. 3D bioprinted tissue constructs involving PBs can offer better insights into the tumor microenvironment and offer platforms for drug screening to advance cancer research. These bioinks enable the incorporation of physiologically relevant cell densities, tissue-mimetic stiffness, and vascularized channels and biochemical gradients in the 3D tumor models, unlike conventional two-dimensional (2D) cultures or other 3D scaffold fabrication technologies. In this perspective, we present the emerging techniques of 3D bioprinting using PBs in the context of cancer research, with a specific focus on the efforts to recapitulate the complexity of the tumor microenvironment. We describe printing approaches and various PB formulations compatible with these techniques along with recent attempts to bioprint 3D tumor models for studying migration and metastasis, cell-cell interactions, cell-extracellular matrix interactions, and drug screening relevant to cancer. We discuss the limitations and identify unexplored opportunities in this field for clinical and commercial translation of these emerging technologies