The Department of State is primarily responsible for the issuance of visas and U.S. passports. The Department of State Web-site offers information about the State Department, visas, passports, U.S. embassies and consulates, and much more. The U.S Department of State (DOS) Bureau of Population, Refugees, and Migration (PRM) operates a Refugee Processing Center (RPC) which tracks refugee admissions and arrival statistics.
The mission of the Department of Labor (DOL), Foreign Labor Certification office, is to permit U.S. employers to hire aliens, on a temporary or permanent basis, provided there aren't U.S. workers "able, willing and qualified" to fill the positions and admission of aliens won't adversely affect American workers. The DOL Website offers an electronic system for filing labor certification applications, official forms relating to employment-based immigration, and pertinent regulations.
The U.S. Citizenship and Immigration Services (USCIS), a bureau in the Department of Homeland Security (DHS), processes immigration services and benefits. In that capacity, it reviews various types of immigration petitions and applications. The USCIS took over these responsibilities from the Immigration & Naturalization Service (INS) when the INS was abolished in 2002. The USCIS Website offers forms, immigration statutes and regulations, immigration handbooks, policy and procedural memoranda, information on USCIS field offices, and much more. Reviews applications for citizenship, green cards and I-9 employment verifications. Generally also has jurisdiction over asylum applications filed by individuals not in removal proceedings (affirmative filings).
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The U.S. Immigration and Customs Enforcement (ICE), the "investigative arm" of the DHS, enforces immigration and customs laws. Check out the Information Library for Fact Sheets on many different topics, Facility Inspections (covering 2018-2019), Forms, Statements, Federal Register Notices and Regulations and library of FOIA request responses.
The ICE Website describes ICE's mission and various activities of ICE agents. There is also a searchable Detainee database.
Image source: US Dept of Homeland Security
The Executive Office for Immigration Review (EOIR), an office in the Department of Justice, is tasked with adjudicating many types of immigration cases, including most removal hearings and appeals from those hearings. The EOIR consists of Immigration Courts, the Board of Immigration Appeals, and the Office of Chief Administrative Hearing Officer. The EOIR Web-site describes the organizational structure of the EOIR and offers official forms and copies of many administrative decisions. EOIR has jurisdiction over asylum applications of individuals in removal proceedings (defensive filings).
Image source: EOIR
The Office of Refugee Resettlement (ORR) is part of the Administration for Children and Families, a division of the U.S. Dept. of Health and Human Welfare. The ORR offers services to refugees and aids in their resettlement, provided they meet certain status and eligibility requirements. They also offer various fact sheets, tool kits and other resources. The ORR homepage also links to additional state refugee programs and services that may be available.
Image source: U.S. Government, public domain