According to the American Nuclear Society's Center for Nuclear Science and Technology Information:
Nuclear medicine and radiology are the whole of medical techniques that involve radiation or radioactivity to diagnose, treat and prevent disease. While radiology have been used for close to a century, "nuclear medicine" began approximately 50 years ago. Today, about one-third of all procedures used in modern hospitals involve radiation or radioactivity. These procedures are among the best and most effective life-saving tools available, they are safe and painless and don't require anesthesia, and they are helpful to a broad span of medical specialties, from pediatrics to cardiology to psychiatry.
You can learn much more about nuclear medicine at the dedicated CNSTI page on the topic-click here to access it.
The US Nuclear Regulatory Commission has oversight over some, but not all, medical uses of nuclear material and technology. To read about the NRC's role and to see what it regulates, click here.
The US Food and Drug Administration regulates a portion of the medical field that uses radioactivity; click here to access the FDA's extensive site portal covering all aspects of what it regulates. You can also find many other useful resources at this link.
(Will Davis for ANS Nuclear Cafe.)