The most common waivers are:
I-601 Waivers: they seek to waive removal for spouses, fiancés and children of U.S. citizens or green card holders. “Extreme hardship” evidence must be presented.
I-601A Waivers: they seek to allow certain relatives of U.S. citizens and green card holders to apply, in advance for a waiver of inadmissibility. If granted it allows the applicant to leave the U.S. and return to their home country to appear at a U.S. Embassy for an immigrant visa interview. The program's advantage is it allows the applicant the chance to return home with some reasonable assurance of getting a waiver and the time out of the country can be just a matter of days. Again, the key element is a showing of extreme hardship to your family.
I-212 Waivers: they seek to allow non-U.S. citizens to apply for early readmission into the U.S. if they were previously removed and they want to return before their statutory exclusionary period expires (they have a desire to return before their 3 or 10-year ban is fulfilled)
Waivers Are Very Fact Specific. Careful Analysis Is Required, and A Well Prepared, Evidence-Filled Submission Needs to Be Made.