Bioprinting is an emerging technology for constructing and fabricating artificial tissue and organ constructs. This technology surpasses the traditional scaffold fabrication approach in tissue engineering (TE). Currently, there is a plethora of research being done on bioprinting technology and its potential as a future source for implants and full organ transplantation. This review paper overviews the current state of the art in bioprinting technology, describing the broad range of bioprinters and bioink used in preclinical studies. Distinctions between laser-, extrusion-, and inkjet-based bioprinting technologies along with appropriate and recommended bioinks are discussed. In addition, the current state of the art in bioprinter technology is reviewed with a focus on the commercial point of view. Current challenges and limitations are highlighted, and future directions for next-generation bioprinting technology are also presented.