The shortage of human organs for transplantation is a devastating medical problem. One way to expand organ supply is to derive functional organs from patient-specific stem cells. Due to their capacity to grow indefinitely in the laboratory and differentiate into any cell type of the human body, patient-specific pluripotent stem (PS) cells harbor the potential to provide an inexhaustible supply of donor cells for transplantation. However, current efforts to generate functional organs from PS cells have so far been unsuccessful. An alternative and promising strategy is to generate human organs inside large animal species through a technique called interspecies blastocyst complementation. In this method, animals comprised of cells from human and animal species are generated by injecting donor human PS cells into animal host embryos. Critical genes for organ development are knocked out by genome editing, allowing donor human PS cells to populate the vacated niche. In principle, this experimental approach will produce a desired organ of human origin inside a host animal. In this mini-review, we focus on recent advances that may bring the promise of blastocyst complementation to clinical practice. While CRISPR/Cas9 has accelerated the creation of transgenic large animals such as pigs and sheep, we propose that further advances in the generation of chimera-competent human PS cells are needed to achieve interspecies blastocyst complementation. It will also be necessary to define the constituents of the species barrier, which inhibits efficient colonization of host animal embryos with human cells. Interspecies blastocyst complementation is a promising approach to help overcome the organ shortage facing the practice of clinical medicine today.