Currently, there is no federal law prohibiting the transference of a firearm by sale, or inheritance, or by gift between two private parties. As such, no background check is required. Federal law only prohibits the transfer if the person receiving the firearm is intending to commit a crime or is knowingly unable to pass a background check as in the case of a known felon seeking a weapon.
Thus, one spouse can buy a licensed gun for their home without the other spouse needing a background check to use it. Or, you can give a gun to someone for their protection if they are under the threat of bodily harm, without that person having go through the up to 3-day background check process before having possession of a newly purchased gun. Or, a hunter may borrow another hunter's firearm to try it out without going through the process of a background check.
And, yes, a gun collector can take his antique collection of firearms to a gun show and sell all or single items to another private party without the need of a background check for each item sold. This fact, of course, is what Democrats and other gun control advocates call the "gun show loophole". Thus, to the average person, the implication is that criminals and potential mass shooters are buying weapons at gun shows in order to mow down people at schools or movie theaters, or for their use in the commission of a crime.
However, the above assumption that criminals and crazed mass killers are buying weapons at gun shows is false, and is a political pretense for having universal background checks for the very same situations that I noted in the second paragraph.
The reality is that criminals don't obtain their weapons at gun shows. 99.9% of guns purchased at those events are sold by federally licensed gun dealers, who by federal law, are required to obtain background checks on every sale or lose their license. In fact, a 2004 Department of Justice survey of 18,000 inmates at federal and state prisons found that only 16.8% or 3024 had a weapon on them at the time of arrest. Of those 3024, only eight-tenths of a percent said it was purchased at a gun show. That's just 24 inmates who bought their weapons at a gun show. Also, 40% said they had bought guns illegally on the streets. Only, 9.9% said they had purchased their guns from a licensed pawn shop or gun retailer.
Gun shows are also not the source for weapons used by mass shooters. In a news article appearing in the New York Times titled "How They Got Their Guns", the writer analyzed the last 14 most horrific mass shootings and found that in every case, the weapons used were legally obtained at gun stores and not gun shows.
So, the bottom line is that gun shows are a minuscule part of this country's gun violence problem, though Democrats still want to use the gun show loophole to their political advantage. They tell their base to blame Republicans for not closing this so-called loophole. A loophole that allows private citizens to exchange guns among themselves; not just at gun shows, but anywhere; the vast majority of which won't be used in the commission of any crime.
Senate Democrats as they demand new gun-control laws: http://www.washingtontimes.com/news/2015/oct/8/armed-guards-protect-senate-democrats-they-demand-/
Gun show loophole: https://www.google.com/search?q=gun+show+loophole&ie=utf-8&oe=utf-8
Justice Department Study: Page 13: Firearm Use By Offenders: Table 14: http://www.bjs.gov/content/pub/pdf/fv9311.pdf
How They Got Their Guns: http://www.nytimes.com/interactive/2015/10/03/us/how-mass-shooters-got-their-guns.html?_r=0