The BBC News website looks at what the procedure involved.

What have the French team done?

They have transplanted skin from a donor on to a 36-year-old woman's face. The new tissue covers her nose, lips and chin - which were all damaged when she was attacked by a dog in January this year.

The operation involves connecting many small blood vessels from the donated tissue to the patient's face.

Has it been tried before?

The procedure has not been tried on a living human before.

However, a plastic surgeon in the US says he has transplanted the face of one dead person onto another dead person and scientists have successfully carried out face transplants on animals, namely rats and dogs.

Surgeons in India have successfully replanted the face of one patient. However, normal appearance was affected and muscles were damaged.

Is the French team the only one working on face transplants?

No. Surgeons in Cleveland, US, announced in September that they planned to interview prospective patients for a face transplant.

In addition, a team led by Dr Peter Butler from the Royal Free Hospital in London and another US team in Kentucky are carrying out research.

What are the medical concerns?

As there have been no human trials of this procedure in live patients, nobody really knows what the long-term effects would be.

Experts have warned there is a real risk that the procedure will not work.

In the short term, clots could form in the donated tissue. And, in the longer term, the immunosuppressants may fail.

The risks of rejection are relatively high. Senior surgeons estimate one in 10 patients could suffer rejection within six weeks.

Up to half could suffer chronic rejection after a year.

Taking immunosuppressants also increase a person's cancer risk, so anyone who considering a face transplant would have to decide whether the benefits outweighed the risks.

And what about the ethical worries?

The second major factor is the psychological effects - both on the patient and on the donor's family.

There are doubts that families would consent to have the face of their loved one removed and transplanted onto someone else.

If they did give permission, how would these families react if they were to meet or see the patient?

For their part, the patient would have to come to terms with the fact that they do not look the way they did before.

They would also have to be comfortable wearing someone else's face. This cannot be taken for granted.

The man who received the world's first hand transplant asked for it to be removed, partly because he didn't like having somebody else's hand.

What would the patient look like?

Nobody really knows. They would not have the same skeleton and facial shape as the donor, so they would not look like them. But neither would they look as they did before.