The "gun show loophole," an exception to the Brady Law -- ironically, the same one that bans felons from being able to buy or posses a firearm also permits the purchase of firearms at gun shows without a background check. More specifically, it does not require a background check if the gun is bought from an unlicensed firearms dealer. As many as half of the dealers at gun shows are unlicensed.
"Data from a national survey of inmates indicated that nearly 80 percent of those who had used a handgun in a crime had acquired it through a transaction with an individual who was not a licensed gun dealer." ~Johns Hopkins Center for Gun Policy and Research.