Scientists are working on making rejection-free organs, using genetically-altered pigs as the donors.
They use a gene editing tool known as crispr to remove some of the pig genes and add certain human genes to make the organ more compatible.
Breeding special pigs for this is ideal, say experts, since their organs are roughly the right size for people.
The science is still extremely experimental, but a heart and a kidney operation have gone ahead.
The two men who agreed to having the procedures were pioneers of this new field of transplantation medicine.
Both have since died but helped advance xenotransplantation - the transplanting of living cells, tissues or organs from one species to another.
Another avenue being explored is growing brand new organs using our own human cells.
Stem cells have the ability to grow into any type of cell or tissue found in the body.
No research group has yet been able to make fully functional, transplantable human organs, but scientists are getting closer.
In December 2020, UK researchers UCL and the Francis Crick Institute rebuilt a human thymus - an essential organ in the immune system - using human stem cells and a bioengineered scaffold.
When transplanted into mice as a test, it appeared to work.
And scientists at Great Ormond Street Hospital in London say they have grown human intestinal grafts using stem cells from patient tissue that could one day lead to personalised transplants for children with intestinal failure.
But these advances are for treating ill health, rather than keeping people alive to 150.