Currently, there are over 120,000 Americans alone who are on the list to get an organ transplant. To meet this high demand for organs such as liver and hearts, scientists have begun experimenting growing these organs inside animals via the addition of human stem cells. Mainly, the research has focused on pig and sheep embryos. Link
It is not leap of logic to guess that this research is extremely controversial. Not only that, but we don't know much about the effects of human organs grown in animals.
But the bigger worry is the instability of human stem cells. Human stem cells have the tendency to specialize and multiply and risk giving the animal human characteristics which could range from physical features...to intelligence.
However, many research labs are moving forward with this research. New technologies are making it possible to genetically engineer pigs and sheep so that they can't develop certain tissue and organs. So what? Well that's how scientists would inject human stem cells into the embryos of such animals and allow the stem cells to grow into the missing human organ, which would then be harvested.
This picture is from the Flickr Account University of Liverpool Faculty of Health & Life Sciences and is licensed under Creative Commons.