The FDA permits the sale of a particular drug only after "field trials" have proven it to be both safe and effective. Typically, these trials involve only adults; it isn't cost-effective for drug makers to conduct trials on children. The presumption is that a drug that is safe for adults is also safe for kids - but this is rarely proven. So when doctors prescribe drugs for children, they're generally doing so without formal FDA approval. Not an ideal situation, to say the least.
The American Academy of Child and Adolescent Psychiatry and the American Academy of Pediatrics have urged the FDA to require field trials for children, but I'm not holding my breath.