Under the GCA, firearms possession by certain categories of individuals is prohibited.

Anyone who is under the age of 18, except with the written permission of their parent or guardian.
Anyone who has been convicted in a federal court of a crime punishable by imprisonment for a term exceeding 1 year, excluding crimes of imprisonment that are related to the regulation of business practices.
Anyone who has been convicted in a state court of a crime punishable by imprisonment for a term exceeding 2 years, excluding crimes of imprisonment that are related to the regulation of business practices.
Anyone who is a fugitive from justice.
Anyone who is an unlawful user of or addicted to any controlled substance.
Anyone who has been adjudicated as a mental defective or has been committed to a mental institution.
Any alien illegally or unlawfully in the United States or an alien admitted to the United States under a nonimmigrant visa.
Anyone who has been discharged from the US Armed Forces under dishonorable conditions.
Anyone who, having been a citizen of the United States, has renounced his or her citizenship.
Anyone that is subject to a court order that restrains the person from harassing, stalking, or threatening an intimate partner or child of such intimate partner.
Anyone who has been convicted of a misdemeanor crime of domestic violence. (See the Lautenberg Amendment.)
A person who is under indictment or information for a crime punishable by imprisonment for a term exceeding one year cannot lawfully receive a firearm. Such person may continue to lawfully possess firearms obtained prior to the indictment or information.

The Brady Handgun Violence Prevention Act of 1993 created a national background check system to prevent firearms sales to such "prohibited persons."