Immigration and naturalization/citizenship records are kept by:

U.S. Citizenship and Immigration Services

However, only historical records are available, mainly for genealogical research purposes. At the USCIS home page click on the History and Geneology link for details on requesting those records.

The National Archive also has searchable online databases of some historical immigration records.

Passenger records of ships carrying immigrants who arrived at Ellis Island in New York from 1892 to 1924 also are available in a searchable online database at the Statue of Liberty-Ellis Island Foundation website.

Naturalization records are filed in civil courts, usually on a county level, and are not available online. See the National Archive section on naturalization records on how to research those records.

Private website, often used for genealogical purposes, might also be a resource for these types of records.

Immigration Courts

Immigration Courts handle cases of people who have been charged with violating immigration laws and thus could be deported. They are not regular courts, but rather are part of the U.S. Department of Justice.

Their proceedings and records generally are not public.

Passports and Visas

Passport and visa records are kept by the U.S. State Department but the records are not publicly available.