Over the years, the field of bioprinting has attracted attention for its highly automated fabrication system that enables the precise patterning of living cells and biomaterials at pre-defined positions for enhanced cell-matrix and cell-cell interactions. Notably, vat polymerization (VP)-based bioprinting is an emerging bioprinting technique for various tissue engineering applications due to its high fabrication accuracy. Particularly, different photo-initiators (PIs) are utilized during the bioprinting process to facilitate the crosslinking mechanism for fabrication of high-resolution complex tissue constructs. The advancements in VP-based printing have led to a paradigm shift in fabrication of tissue constructs from cell-seeding of tissue scaffolds (non-biocompatible fabrication process) to direct bioprinting of cell-laden tissue constructs (biocompatible fabrication process). This paper, presenting a first-time comprehensive review of the VP-based bioprinting process, provides an in-depth analysis and comparison of the various biocompatible PIs and highlights the important considerations and bioprinting requirements. This review paper reports a detailed analysis of its printing process and the influence of light-based curing modality and PIs on living cells. Lastly, this review also highlights the significance of VP-based bioprinting, the regulatory challenges and presents future directions to transform the VP-based printing technology into imperative tools in the field of tissue engineering and regenerative medicine. The readers will be informed on the current limitations and achievements of the VP-based bioprinting techniques. Notably, the readers will realize the importance and value of highly-automated platforms for tissue engineering applications and be able to develop objective viewpoints towards this field.