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Some people who have lived in the U.S. as permanent residents for a long time will want to become citizens, which gives you all of the rights of U.S. citizenship (including the right to vote), and removes almost all of the uncertainty from your immigration status, allowing you to leave the country and return as you please.
Everyone born in the U.S. or in a U.S. territory (including American military bases in foreign countries, American embassies, or American-flagged ships at sea) is automatically a U.S. citizen, regardless of the citizenship or immigration status of their parents. The same applies to children born to two U.S. citizen parents, anywhere in the world.
To apply to become a naturalized U.S. citizen, you must have been in the U.S. as an LPR for at least 5 years, you must have lived in the U.S. for at least half of your time as an LPR, you must be at least 18 years old, and you must be of good moral character (this is typically determined by a person's criminal record, or lack thereof).
Once you apply for citizenship, you will have to take a citizenship exam, testing your understanding of the basic workings of the U.S. government. You will also have to go through an interview, which will be conducted in English.