Here are the main types of immigration statuses:

h thumb u visaU Visa
The U Visas is an immigration option for victims of certain serious crimes (such as domestic violence, human trafficking, and felonious assault). In order to qualify, victims must show that they assisted law enforcement and suffered as a result of the crime. Benefits include employment authorization and a path to permanent residency.
h thumb vawViolence Against Women Act (VAWA)
VAWA allows immigrant victims of domestic violence who are married or have recently been married to US citizens or legal permanent residents to self petition for permanent residence. VAWA is also an option for abused parents of US citizens and abused children of US citizens or permanent residents. Both men and women are eligible to file for VAWA.
h natural disasterTemporary Protected Status (TPS)
Due to country conditions such as ongoing conflict and natural disaster, the Department of Homeland Security temporarily designates certain countries with TPS status that allows immigrants from those countries to stay in the US and obtain work permits.
h thumb sijsSpecial Immigrant Juvenile Status (SIJS)
SIJS is an option for immigrant children that have been abused, abandoned or neglected. SIJS includes a path to permanent residence.
h thumb asylumAsylum
Immigrants who have a reasonable fear of persecution in their home country due to their race, religion, nationality, political opinion, or membership in a certain social group may be eligible for asylum. In general, the asylum application has to be submitted within a year of arrival into the US.