The Federal Bureau of Investigation (FBI) is the domestic intelligence and security service of the United States, and its principal federal law enforcement agency. Operating under the jurisdiction of the US Department of Justice, the FBI is also a member of the U.S. Intelligence Community and reports to both the Attorney General and the Director of National Intelligence. A leading U.S. counter-terrorism, counterintelligence, and criminal investigative organization, the FBI has jurisdiction over violations of more than 200 categories of federal crimes.
Role in Gamergate
July 2014 meeting
The San Diego FBI approached International Game Developers Association chair Kate Edwards at the Comic-Con in July 2014 to discuss the harassment of women game developers. 
Sanc gave the FBI enough information to track down Anita Sarkeesian harasser Mateus Prado Sousa in Brazil. The FBI could not legally forward the case to Brazilian authorities without Sarkeesian's permission, which she refused to give. 
On November 5, 2014, Oliver Campbell claimed that "FBI and DHS are aware of and KNOW that at least two certain individuals sent themselves threats." On November 7, Campbell said that he knew of an FTC investigation but could not confirm whether the FBI was investigating.
An Anonymous video accused Bill Waggoner Crew members CommanderXanon and Laurelai of being FBI informants. 
Other investigating agencies
On November 13, 2014, NPR reported that the local police department of Arlington, Massachussetts is "in the middle of a high-profile investigation into the online harassment of Brianna Wu." Arlington police chief Frederick Ryan is quoted as saying it can take as long as 30-45 days to get an IP address from Twitter.