A K-3 spouse visa is filed together with an immediate relative petition.  They allow the married foreign spouse of a U.S. citizen to enter the United States to permanently reside in the country.

Adjustment of status allows the married spouse of a U.S. citizen who was lawfully admitted or paroled into the U.S. to apply for permanent resident status without having to leave the United States.

An I-601 waiver allows you to waive the “unlawful presence” or “misrepresentation” grounds of inadmissibility.  You must prove that your U.S. citizen or permanent resident spouse or parent would suffer “extreme hardship” if you two cannot be united.

The I-212 waiver allows you to apply for early readmission into the U.S. after you were previously removed and before you stayed the required amount of time outside the U.S.

I-601 A Provisional Waiver allows certain immediate relatives of U.S. citizens to apply for a provisional waiver of the unlawful presence ground of inadmissibility while still in the United States if they can demonstrate that being separated from their U.S. citizen spouse or parent would cause that U.S. citizen relative ”extreme hardship”.