The idea is that using a patient's own stem cells to grow new body parts avoids the whole issue of rejection as well as waiting for a donor.
Dr Anthony Atala, director of the Institute for Regenerative Medicine at the Wake Forest Baptist Medical Center in North Carolina, US, has made breakthroughs in building bladders and urethras.
He breaks tissue-building into four levels of complexity.
1. Flat structures, such as the skin, are the simplest to engineer as they are generally made up of just the one type of cell.
2. Tubes, such as blood vessels and urethras, which have two types of cells and act as a conduit.
3. Hollow non-tubular organs like the bladder and the stomach, which have more complex structures and functions.
4. Solid organs, such as the kidney, heart and liver, are the most complex to engineer. They are exponentially more complex, have many different cell types, and more challenges in the blood supply.
"We've been able to implant the first three in humans. We don't have any examples yet of solid organs in humans because its much more complex," Dr Atala told the BBC.
Previously we had reported that an injection of stem cells given alongside a kidney transplant could remove the need for a lifetime of drugs to suppress the immune system
Wake Forest researchers have produced liver organoids which can break down drugs.
Dr Atala said: "The challenge for us is - how do we scale up?"
Bioprinting, just like an office printer except it "prints" cells layer by layer, has been used to "print" a kidney.
Dr Atala said: "The strategies are out there to someday be able to target every organ in the body we are not there yet. We are nowhere near there yet.
"But the goal of the field is to keep on advancing the number of tissues that we can target."
Of course growing a hand is even more challenging than anything being tried in laboratories so far. Will it ever be possible?
"You never say never, but certainly it's something I will most likely not see in my lifetime," Dr Atala concluded.
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