Three-dimensional (3D) printing of human tissues and organ has been an exciting research topic in the past three decades. However, existing technological and biological challenges still require a significant amount of research. The present review highlights these challenges and discusses their potential solutions such as mapping and converting a human organ onto a 3D virtual design, synchronizing the virtual design with the printing hardware. Moreover, the paper discusses in details recent advances in formulating bio-inks and challenges in tissue construction with or without scaffold. Next, the paper reviews fusion processes effecting vascular cells and tissues. Finally, the paper deliberates the feasibility of organ printing with state-of-the-art technologies.