The first accounts of phantom limbs came from a man by the name of S. Weir Mitchell who observed Civil War amputees at a hospital in Philadelphia. He wrote a book about his curious dealings with amputees, some of who insisted that they could still feel their amputated limb. His accounts were the first documented cases of phantom limbs. There has now been extensive study of the phantom limb sensation but technology limits what can be learned from direct physical study of the brain, thus the theories of phantom sensation all arise from the analysis of case studies.
Here are some interesting facts about phantom sensations:
Approximately 80% of amputees have some phantom limb sensations.
The phantom sensation can occur right after the amputation or many months or years later.
Phantom pain are not typically experienced by children under the age of 4.
Intensity, duration, severity, quality and chroncity all are variable and are not static from patient to patient.
Many phantom limb sensations occur after some injury to the site of the amputation. Thus, a person who was born without a limb, and did not experience any type of phantom sensation could suddenly find themselves experiencing one if some type of injury occurred to the stump.
Phantom limbs help with the use of prosthetics. It's easier to use some type of prosthetic device if there are phantom sensations associated with the limb.
This link will chronicle a number of case studies. If you've read the associated with phantom limbs, then this section will help you understand the phenomenon.