Tissue engineers have been inching closer to building a kidney from stem cells in the past couple of years. Here is a recent example of the ongoing work in this field:
Investigators can produce tissues similar to immature kidneys from simple suspensions of embryonic kidney cells, but they have been unsuccessful at growing more mature kidney tissues in the lab because the kidneys' complicated filtering units do not form without the support of blood vessels.
Now, from suspensions of single kidney cells, [researchers] have for the first time constructed "organoids" that can be integrated into a living animal and carry out kidney functions including blood filtering and molecule reabsorption. Key to their success was soaking the organoids in a solution containing molecules that promote blood vessel formation, then injecting these molecules into the recipient animals after the organoids were implanted below the kidneys. The organoids continued to mature and were viable for three to four weeks after implantation.