Especially nowadays, many previously attainable ways to emigrate to the United States are either off limits or so locked down with restrictions that some people feel stuck. However, marriage to a U.S. citizen does allow a person to obtain permanent residency in most cases, as long as you can establish your bonafides as an actual couple. Before you marry, it is still a good idea to ensure that you understand what your rights are and the obligations you must fulfill before any status is granted.
The most common ways for someone to bring over a foreign spouse is to petition for an immigrant visa if they are already married, or a K visa if they are engaged. A K visa is a nonimmigrant visa, not an immigrant visa, and all it does is allow the foreign spouse to enter the U.S. and get married. It does not permit them to stay beyond 90 days unless the wedding has taken place. While the foreign spouse is obtaining their K visa, the U.S. citizen spouse should be filing a Petition for Alien Relative, which then allows them to adjust their status from within the country, as opposed to having to go back to their homeland.
None of this process is possible, however, if the foreign national does not meet at least some of the requirements for an immigrant visa and bring all the appropriate documentation the consulate requires. If the person is inadmissible, they must first file for a waiver of unlawful presence (or whatever ground is making them inadmissible, such as having a criminal record), and then seek to use the K visa. Some grounds for inadmissibility do not have a waiver available, such as espionage, or being a member of the Nazi Party or any other group participating in a genocide....