Uniting U.S. citizens and lawful permanent residents (green card holders) with their overseas family members is an important goal of U.S. immigration law. But that doesn't mean that every relation of a U.S. citizen or permanent resident will qualify for a U.S. green card. The law sets strict guidelines for which family relations are green-card eligible—and in some cases, for how many people will be allowed into the U.S. per year based on that category. The result is that you'll need to plan for possible delays, and perhaps implement step-by-step strategies for ultimately reuniting your family in the United States, as described here.
An unlimited number of green cards can be issued to immigrants who are immediate relatives of U.S. citizens, which means they need not deal with waiting lists based on high demand. Immediate relatives are defined as:
The U.S. citizen sponsor starts the immigration process by petitioning on Form I-130, issued by U.S. Citizenship and Immigration Services (USCIS). After that, the immigrant submits additional paperwork and most likely goes through "consular processing" to receive a U.S. immigrant visa (the equivalent of a green card). Or in some cases, where the immigrant is already in the U.S. (ideally in lawful immigration status), that person need not leave, but can apply to USCIS for "Adjustment of Status" on Form I-485 and attend an interview at a USCIS office in order to receive permanent residence. In fact, it's possible in many immediate-relative adjustment cases for the family to submit the I-130 and I-485 packets to USCIS all at once, or "concurrently." (Also see Getting a Green Card: Consular Processing vs. Adjustment of Status.)
Fiancé(e)s of U.S. citizens are also just a few steps away from a green card. But if the fiancé is overseas and the couple wishes to hold the marriage in the U.S. before applying for a green card, the first step is to apply for a temporary (90-day) U.S. visa called a K-1 fiancé visa. After the marriage, the immigrant can apply directly to USCIS for "Adjustment of Status" on Form I-485 and, following the USCIS interview, receive what's called "conditional permanent residence," which should eventually lead to permanent residence.
Certain other family members of U.S. citizens or permanent residents are also eligible for U.S. green cards. However, only a limited number of green cards are available to these applicants. They typically have to wait many years to get them, based on their place in the following preference categories:
As described above, the U.S. family member must start the process by petitioning for the immigrant on Form I-130. Following USCIS's approval, however, the intending immigrants might have to wait several years until their "priority date" is current and they can move forward (also following the same process described above).
U.S. immigration law offers no direct way to obtain U.S. green cards for one's grandparents, aunts, uncles, nieces, nephews, and more extended relations—unless you can create a chain of relationships so that a more immediate family member can petition for them.
For example, instead of petitioning for a grandparent, a U.S. citizen could petition for his or her parents; and they could, after receiving a green card and eventually U.S. citizenship, petition for their parents (your grandparents). But this strategy almost always requires long-term planning, because obtaining both a green card and eventually U.S. citizenship tends to take several years, depending on a variety of factors.
One important variable is that, in the visa categories subject to annual limits (in what is called the "preference" categories), the number of people applying almost always exceeds the supply of available visa numbers (green cards). The result is that applicants must typically wait a long time until a visa number is available. The average wait is from five to 25 years, depending on the visa category and the country from which the immigrant is applying (due to per-country limits). In recent years, however, there have been visas available in category 2A with little to no wait.
Keep in mind that every immigrant must fit the eligibility criteria all the way up through their approval for adjustment of status or entry to the U.S. on an immigrant visa. If, for example, someone immigrating as an unmarried child gets married in between receiving their U.S. visa and entering the United States, they will be denied entry. See an immigration attorney if you encounter complications like these.
Regardless of whether a foreign national has one of the qualifying relationships to a U.S. citizen or permanent resident, they won't automatically be approved for U.S. lawful permanent residence. A major hurdle to overcome is proving that they are not "inadmissible," or disqualified from an immigrant visa for reasons to do with their health, record of crimes or immigration violations, financial ability to stay off government assistance in the United States, and so on. See Who Can't Get Into the United States Under U.S. Immigration Law? for details.