The rising global incidence of cancer and high attrition rates of anticancer drugs make it imperative to design novel screening platforms to increase the success rate of chemotherapeutic agents. Advances in cell culture models from two-dimensional to three-dimensional platforms, along with microfluidics, have resulted in the creation of tumor-on-a-chip technology, which enables high-throughput molecular screening and helps to simulate the dynamic tumor microenvironment. Furthermore, advancements in bioprinting have allowed the structural and physiological aspects of the tumor to be recreated accurately and help to mimic cell-cell interactions and cell-extracellular matrix. This paper provides a comprehensive review of three-dimensional bioprinting to fabricate a tumor-on-a-chip platform to advance the discovery and screening of anticancer agents and provides a perspective on the challenges and future directions associated with the adoption of this technology to advance cancer research.