There are a number of waivers written into section INA 212 to help a person overcome a past overstay (3/10-year bars triggered), unlawful entries etc.

I-601A waiver:
You can only use this waiver if you entered without inspection or are unlawfully present in the United States as a result of overstaying your visa and you have no other inadmissibility issues. The purpose of this waiver is to permit your past to be forgiven, and you only depart the States to have your interview at your home countries consulate and re-enter with a green card. If this waiver is not approved, then you don’t depart the United States.

The qualifying relatives for the I-601A waiver are the following:
The qualifying relative must be either a U.S. citizen or a lawful permanent resident, spouse, child, son, or daughter.
The purpose of the I-601A waiver is to waive, to forgive you of the unlawful presence ground of inadmissibility, or it waives how you entered. If you entered without inspection, it waives this also. If you have any other ground of inadmissibility, then you are not permitted to file for this waiver.
Once the underlying I-130 Petition for Alien Relative application is approved, or your I-360 or your I-140 is approved, then you can file the I-601A waiver of inadmissibility with USCIS. If the I-601A waiver is denied, your options are to appeal the I-601A waiver or refile a new I-601A waiver. If the I-601A waiver is approved, then NVC and your home countries embassy will send you information for further documents required for your green card interview.

I-601waiver:
This waiver overcomes different inadmissibility issues.
If you are physically inside the States, you can file this waiver concurrently with your I-485, adjust status petition. If you are physically outside the States and the consulate officer is stating, you need this waiver at your green card interview. The consulate will not adjudicate this waiver. Instead after your embassy interview you will have to file the I-601 inadmissibility waiver with USCIS. The processing times for USCIS to adjudicate these inadmissibility waivers is at least 12 months.