The Brady Handgun Violence Prevention Act of 1993 requires licensed gun dealers to perform background checks. Background checks are not required for private gun sales (though, as mentioned above, it's still a crime to knowingly sell a gun to someone with a criminal record). To ensure privacy, Section 103(i) of the Act prevents the Federal government from keeping the names submitted for background checks, or using this information to create any sort of registry of gun owners.
From 1994 to 2004, the Federal Assault Weapons Ban prohibited the sale and manufacture of semi-automatic weapons (in which each pull of the trigger fires one shot) with various military features such as large-capacity magazines and pistol grips. It was still legal to keep previously owned weapons. The law expired in 2004 due to a built-in "sunset" clause.
These federal laws set minimum standards, but many states have also passed various types of gun laws. These laws determine which weapons are legal to own, and also set requirements on sales, background checks, storage, open and concealed carrying permits, and sentencing of gun-related crimes.
What could be done to reduce gun violence?
The firearms debate usually revolves around "gun control" -- that is, laws that would make guns harder to buy, carry, or own. But this is not the only way of reducing gun violence. It is possible to address gun use instead of availability. For example, Project Exile moved all gun possession offenses in Richmond, Virginia, to federal courts instead of state courts, where minimum sentences are longer. Policies like these, which concern gun use, are sometimes said to operate on gun "demand," as opposed to gun control laws, which affect "supply."
Similarly, while the idea of new laws gets most of the attention, some projects have focused on enforcing existing laws more effectively, or changing policing strategies the way Boston's Operation Ceasefire did in the 1990s. In fact, launching community-based programs has proven to be one of the most effective strategies for reducing gun violence. (See: What has worked, below.)
There have also been programs based on other principles, such as public safety education and gun buy-back campaigns. The White House proposals (see below) address both gun access and gun use, and include both new laws and enhanced enforcement of existing laws.
(More: Aiming for Evidence-based Gun Policy, Phillip Cook and Jens Ludwig)
Would fewer guns result in less gun violence?
Suppose it were possible to reduce the number of guns in circulation, or make it harder for people to get a gun. Would gun violence go down?
Although countries that offer easier access to guns also have more gun violence, at least among developed nations, this doesn't necessarily mean that more guns cause more deaths. People may own more guns in dangerous places because they want to protect themselves. It's also possible that gun ownership is a deterrent to crime, because criminals must consider the possibility that their intended victim is armed.
Economist John Lott did extensive work on this question in the late 1990s, culminating in his 1998 book More Guns, Less Crime. He studied the effect of right-to-carry laws by examining violent crime rates before and after they were implemented in various states, up until 1992, and concluded that such laws decreased homicides by an average of 8%. Lott's data and methods have been extensively reviewed since then. A massive 2004 report by a 16-member panel of the National Research Council found that there was not enough evidence to say either way whether right-to-carry laws affected violence. In 2010, different researchers re-examined Lott's work, the NRC report, and additional data up through 2006, and reaffirmed that there is no evidence that right-to-carry laws reduce crime.
Meanwhile, other studies have suggested that reduced access to guns would result in less crime. These studies compared homicide rates with gun availability in various states and cities. The most comprehensive estimate is that a 10% reduction in U.S. households with guns would result in a 3% reduction in homicides. Internationally, the effect of reductions in gun ownership might be much larger. This might have to do with the large number of guns already available in the U.S.: Any reduction in gun violence hinges on whether gun control laws would actually make it prohibitively difficult to get a gun.
(More: Gun Rhetoric vs. Gun Facts, Factcheck.org; The Impact of Right to Carry Laws and the NRC Report: Lessons for the Empirical Evaluation of Law and Policy, John J. Donohue III, Abhay Aneja, and Alexandria Zhang)
Does gun control result in fewer guns?
In principle, it's not necessary to keep guns away from everyone, just those who would misuse them. Background checks are promising because a high fraction of future killers already have a criminal record. In one study in Illinois, 71% of those convicted of homicide had a previous arrest, and 42% had a prior felony conviction.
Yet current federal gun regulation (see above) contains an enormous loophole: While businesses that deal in guns are required to keep records and run background checks, guns can be transferred between private citizens without any record. This makes straw purchases easy. In other words, these laws may generally make guns harder to come by, but those who really want them can still obtain them through private sales.
Also, although it's generally illegal to sell guns across state lines, in practice this is very common. There's abundant evidence that under the current system, guns flow easily between legal and illegal markets. Washington, D.C,. banned all handguns in 1976, and Chicago did the same in 1982. In neither case did the percentage of suicides using firearms -- considered a very good proxy for general gun availability -- fall significantly.