[Not quite TLDR, but call it Cliff Notes... most of this is directly quoted, but I have done some editorializing.]

In 2001, some researchers at UCLA discovered that fat cells (adipose) contain an abundance of adult stem cells. Separate out the mature fat cells and the remaining cells, which they called PLA, can be coaxed into forming bone and cartilage.

Jalees Rehman and Keith March at Indiana University decided to see if they could use these cells to repair the heart and grow new blood vessels. Their "goal was to convert fat stem cells from liposuction aspirates into cardiovascular cells, such as cardiomyocytes or endothelial cells that form the lining of all blood vessels."

Over the course of the next year, although they had a few cultures that did seem to behave like cardiac cells, they couldn't reliably produce them.

The team learned of reports that adult bone marrow mesenchymal stem cells released growth factors that nourished and accelerated the regeneration of neighbouring cells. Researchers were increasingly calling these stem cells ‘stromal cells’, from the Latin ‘stroma’ for mattress or covering, to signify their support function.

They decided to try growing PLA cells side by side with endothelial cells and studying what occurred. When they added PLA cells to the gels, the growth of the blood-vessel-like tubes increased several-fold. "Analysing the PLA genes and proteins they produced, we found not one, but a multitude of factors that promoted survival, regeneration and growth of blood vessels. Synergy between all the factors likely explained why they were so effective. These growth factors not only activated the growth of endothelial cells, they also made endothelial cells more resilient to stress. In the aftermath of this work, I decided to rename PLA cells ‘adipose stromal cells’ (ASCs), to emphasise the fact that it was their ‘stromal’ or caretaker function that aided in their ability to form blood vessels."

Especially important was the discovery that ASCs did not just blindly churn out growth factors. Their productivity was regulated by the cell’s ability to sense oxygen. When placed in a low-oxygen environment, the ASCs doubled or tripled production of factors necessary for the growth of blood vessels. Since heart and limb muscle tissues of patients with blood vessel blockages suffer from low oxygen levels; implanting ASCs that released therapeutic molecules based on oxygen levels seemed almost too good to be true.

They did a preliminary test on mice, and met with success. (why does it always work on mice?!) They cut off blood supply to the lower parts of the legs of experimental mice. Half the mice then received an injection of human ASCs into the leg muscle. We observed an astonishing recovery of blood flow through new blood vessels in ASC-treated mice, but not our controls.

Since then, clinical trials are proceeding somewhat rapidly, in part due to FDA exemptions for treatment with one’s own cells, as long as modifications are no more than minor and cells are re-injected during the same procedure. "The irony is that the less effort such clinics spend on processing and characterising the cells they are injecting into patients, the more likely they are to get away with it." These exemptions may encourage treating with under-processed cells, since too much processing voids the exemption, but it remains to be seen if theres low-hanging fruit here, or if scientists will have to work much harder to refine the processing in order to see actual clinical benefit from injecting ASC.