You can obtain an I-601A waiver of inadmissibility, which will overcome a 3-year or 10-year bar, even if you have other inadmissibility issues such as a serious criminal conviction. If you don’t resolve these issues before you leave the U.S. (by filing for a I-601 waiver), your waiver could be revoked while you are overseas, resulting in you being unable to return to the U.S. despite having received an I-601A waiver. Some grounds of inadmissibility cannot be waived at all.
Recently there has been an increase in the number of approved I-601A applicants who have been denied permission to return to the US on the grounds that they are likely to become a “public charge”, which means that they are likely to rely on public assistance such as welfare payments in order to support themselves.
The best practice is to have someone, preferably a lawyer, review your application before you send it.