The FBI's power to arrest is no longer limited to the U.S. They have 63 offices overseas with reach into 180 countries, according to the FBI.

They are located in U.S. embassies.

https://www.fbi.gov/contact-us/legal-attache-offices

When did Congress approve the FBI's expansion of its offices and authority overseas?

https://www.fbi.gov/about/leadership-and-structure/international-operations

Here are the FBI's eleven offices in Europe:

Berlin, Germany
American Embassy: 011-49-30-238-5174
Frankfurt Suboffice
American Consulate: 011-49-69-7535-0
Nations covered: Germany
Bern, Switzerland
American Embassy: 011-41-31-357-7011
Nations covered: Liechtenstein, Switzerland
Brussels, Belgium
American Embassy: 011-32-2-512-5519
Nations covered: Belgium, Luxembourg, U.S. Mission to NATO and the EU
Copenhagen, Denmark
American Embassy: 011-45-3341-7100
Stockholm, Sweden Suboffice
America Embassy: 011-46-8-783-5488
Nations covered: Denmark, Faroe Island, Finland, Greenland, Iceland, Norway, Sweden
London, England
American Embassy: 0-11-44-207-894-0007
Nations covered: United Kingdom ( England, Northern Ireland, Scotland, Wales), Republic of Ireland, Channel Islands (Guernsey, Jersey)
Madrid, Spain
American Embassy: 011-34-91-587-2200
Nations covered: Andorra, Gibraltar, Portugal, Spain
Paris, France
American Embassy: 011-33-1-4312-2222
Lyon Suboffice (INTERPOL)
Nations covered: France, Monaco
Prague, Czech Republic
American Embassy: 011-420-2-5702-2000
Nations covered: Czech Republic and Slovakia
Rome, Italy
American Embassy: 011-39-06-4674-2710
Nations covered: Italy, Malta, San Marino, Vatican City
The Hague, Netherlands
American Embassy: 011-31-70-310-2264
Nations covered: Netherlands, U.S. Mission to Europol
Vienna, Austria
American Consulate: 011-43-1-313-39-2155
Nations covered: Austria, Croatia, Slovenia

https://www.fbi.gov/contact-us/legal-attache-offices/europe

The FBI also has offices in Africa, South and Central America, Asia, and the Middle East. They are marked in red on the attached world map:

https://www.fbi.gov/contact-us/legal-attache-offices

Loretta Lynch, Attorney General for the Obama Administration, said the Justice Department, Secret Service, and FBI were making arrests and prosecuting crimes internationally.

https://www.justice.gov/opa/speech/attorney-general-loretta-e-lynch-addresses-european-cybercrime-center-europol

In a speech at the Hague, Netherlands, Lynch announced the Justice Department was assigning a second prosecutor within the European Cyber-Crime Centre, also known as EC3.

Lynch also said the FBI is placing "three new permanent Cyber Assistant Legal Attachés (offices) in foreign offices including London, Ottawa and Canberra, Australia."

https://www.scmagazine.com/us-dept-of-justice-placing-more-agents-overseas-to-repel-cyber-crime/article/533593/