BACKGROUND The worldwide demand for the organ replacement or tissue regeneration is increasing steadily. The advancements in tissue engineering and regenerative medicine have made it possible to regenerate such damaged organs or tissues into functional organ or tissue with the help of 3D bioprinting. The main component of the 3D bioprinting is the bioink, which is crucial for the development of functional organs or tissue structures. The bioinks used in 3D printing technology require so many properties which are vital and need to be considered during the selection. Combination of different methods and enhancements in properties are required to develop more successful bioinks for the 3D printing of organs or tissue structures. METHODS This review consists of the recent state-of-art of polymer-based bioinks used in 3D printing for applications in tissue engineering and regenerative medicine. The subsection projects the basic requirements for the selection of successful bioinks for 3D printing and developing 3D tissues or organ structures using combinations of bioinks such as cells, biomedical polymers and biosignals. Different bioink materials and their properties related to the biocompatibility, printability, mechanical properties, which are recently reported for 3D printing are discussed in detail. CONCLUSIONS Many bioinks formulations have been reported from cell-biomaterials based bioinks to cell-based bioinks such as cell aggregates and tissue spheroids for tissue engineering and regenerative medicine applications. Interestingly, more tunable bioinks, which are biocompatible for live cells, printable and mechanically stable after printing are emerging with the help of functional polymeric biomaterials, their modifications and blending of cells and hydrogels. These approaches show the immense potential of these bioinks to produce more complex tissue/organ structures using 3D bioprinting in the future.