"Congress has broad plenary authority to determine classes of aliens who may be admitted into the United States and the grounds for which they may be removed. Pursuant to the Immigration and Nationality Act (INA), as amended, certain conduct may either disqualify an alien from entering the United States ('inadmissibility') or provide grounds for his or her removal/deportation. Prominently included among this conduct is criminal activity. 'Criminal activity' comprises acts violative of federal, state, or, in many cases, foreign criminal law. It does not cover violations of the INA that are not crimes, most notably, being in the U.S. without legal permission. Thus, the term 'illegal alien' - an alien without legal status - is not synonymous with 'criminal alien.' Most crimes affecting immigration status are not specifically mentioned by the INA, but instead fall under a broad category of crimes, such as 'crimes involving moral turpitude or aggravated felonies'. In addition, certain criminal conduct precludes a finding of 'good moral character' under the INA, which is a requirement for naturalization and certain types of immigration relief."
CRS Report for Congress, RL32480