Being able to market the drug doesn't mean you're out of the woods yet! During a drug's development, you've probably given the drug to hundreds or thousands of subjects, and no serious safety concerns have been raised. But if 1,000 subjects have taken the drug without a single catastrophic adverse event, then that only means that the rate of these kinds of events is probably less than 1 in 1,000.
When your drug hits the market, tens of millions of people may use it; if the true rate of catastrophic events is, for example, 1 in 2,000, then there will be about 5,000 of those catastrophic events in 10 million users. (Does the term class action lawsuit come to mind?)
If the least inkling of possible trouble (or a signal, in industry jargon) is detected in all the data from the clinical trials, the FDA is likely to call for ongoing monitoring after the drug goes on the market. This process is referred to as a risk evaluation mitigation strategy (REMS), and it may entail preparing guides for patients and healthcare professionals that describe the drug's risks.
The FDA also monitors the drug for signs of trouble. Doctors and other healthcare professionals submit information to the FDA on spontaneous adverse events they observe in their patients. This system is called the FDA Adverse Event Reporting System (FAERS). FAERS has been criticized for relying on voluntary reporting, so the FDA is developing a system that will use existing automated healthcare data from multiple sources.
If a drug is found to have serious side effects, the official package insert may have to be changed to include a warning to physicians about the problem. This printed warning message is surrounded by a black box for emphasis, and is (not surprisingly) referred to as a black-box warning. Such a warning can doom a drug commercially, unless it is the only drug available for a serious condition.
And if really serious problems are uncovered in a marketed drug, the FDA can take more drastic actions, including asking the manufacturer to withdraw the drug from the market or even reversing its original approval of the drug.