Any American MD can ask the FDA for "expanded access" to use a medication not approved by the FDA. 99% of the time the FDA grants expanded-access requests.

However, a recent review in NEJM explained how it is time consuming and expensive to apply for expanded-access and often the pharmaceutical companies refuse to distribute the drugs even after the FDA grants expanded-access.

http://www.nejm.org/doi/full/10.1056/NEJMhle1409465

"Compassionate use" is a separate, but related concept with different rules than "expanded access". And in the EU expanded access is often called "named-patient".

Yes. My wife was given medication not FDA approved by her doctor. She had to order it from a pharmacy in Canada, but it was all legit. The (US) doctor wrote her a script and filled out some sort of paperwork for the government, as I understand it.

And no, her doctor isn't some quack who regularly prescribes unapproved medicine. Apparently this particular drug is approved in Canada and Europe, but the company that makes it is small enough that they haven't yet decided to apply for FDA approval because of the cost. (Or at least, that's what I've been told.)

Americans can obviously use drugs approved in Europe in Europe; drugs approved in Europe but not the USA cannot generally legally be imported, sold, or prescribed in the USA, however.