The Gun Control Act of 1968 focuses on commerce. It prohibits mail-order sales of weapons and requires anyone in the business of selling guns to be federally licensed and keep permanent sales records.
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.
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. (thoughit'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 with various military features. It was still legal to keep previously owned weapons. The law expired in 2004 due to a built-in sunset clause.