Many individuals are barred from obtaining immigrant visas based on what are called grounds of inadmissibility. Such individuals must obtain a waiver in order to legally enter the United States. A very common bar is based on unlawful presence in the United States. In that case, an individual may apply for a waiver if their spouse or parent is a U.S. citizen or permanent resident, and they would experience extreme hardship if the applicant was not allowed to return to the United States.
An individual who has been the victim of certain serious criminal activity, has suffered substantial abuse as a result, and has been helpful to law enforcement in the investigation, may be eligible to apply for a U visa. Unlike most visa categories, a U visa is available to individuals currently without lawful immigration status, without the need for a hardship waiver appointment in their country of origin. This visa may be granted for up to four years. After three years the individual may be able to apply for permanent residency.
This should not be considered an exhaustive list, but is provided as a general orientation to common immigration opportunities.