Tissue engineering has been a promising field of research, offering hope for bridging the gap between organ shortage and transplantation needs. However, building three-dimensional (3-D) vascularized organs remains the main technological barrier to be overcome. Organ printing, which is defined as computer-aided additive biofabrication of 3-D cellular tissue constructs, has shed light on advancing this field into a new era. Organ printing takes advantage of rapid prototyping (RP) technology to print cells, biomaterials, and cell-laden biomaterials individually or in tandem, layer by layer, directly creating 3-D tissue-like structures. Here, we overview RP-based bioprinting approaches and discuss the current challenges and trends toward fabricating living organs for transplant in the near future.