As defined by the U.S. Department of Justice, international extradition is the formal process by which a person found in one country is surrendered to another country for trial or punishment. The process is regulated by treaty and conducted between the Federal Government of the United States and the government of a foreign country. 
It differs both from extraordinary rendition in international relations, as well as domestic interstate extradition U.S.). Extraordinary rendition may still involve an overt process by which the person is surrendered to another country by formal but not judicial methods, or may, as used by the George W. Bush Administration, be a secret process.
In extradition, sometimes also called "rendition", a foreign government has to submit a formal extradition request, which the captive has an opportunity to challenge, in the justice system. Normally, an extradition treaty must exist between the countries.
In the United States, extradition requests can be turned down, by the judicial branch, even if the executive branch is in favor of the foreign nation's request. The judiciary can dismiss an extradition request if the charges the foreign government has leveled against the captive are not crimes in the United States. The judicial branch can dismiss an extradition request if the captive has a reasonable fear of facing cruel and unusual punishment if he or she was extradited, or if they had a reasonable fear they would not face a fair trial.
- , USAM Chapter 9-15.000, International Extradition and Related Matters, US Attorneys' Criminal Resource Manual, U.S. Department of Justice