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To enter the U.S. permanently, a person will have to apply for status as a lawful permanent resident (LPR). An LPR has many of the benefits of citizenship – they can leave the country for any amount of time and return without any issues, and they can stay in the country as long as they like.
In almost all situations, the petition to become a permanent resident must be made by someone other than the person who wishes to immigrate, such as an employer or close family member who is already a U.S. citizen or LPR. The process of becoming an LPR can often take years, especially if the person coming to the U.S. is outside the country when they're applying.
If you are already in the country on a "green card" (as an LPR), you can petition to have close family members (spouse and/or children) admitted to the country on a non-immigrant visa. However, there is a quota setting a maximum number of such visas issued each year, and a huge backlog, so this process can take years. If you are a citizen, you can do the same for non-citizen relatives, but the process is different and can take as little as 6 months.