Although U.S. Congress made it perfecly clear that in order for any criminal offense to qualify as an "aggravated felony", it must be a " crime punishable by imprisonment for a term exceeding one year", some circuit courts have decided to ignore this.  For example, in United States of America v. Winston C. Graham, 169 F.3d 787 (3rd Cir. 1999), the Third Circuit Court of Appeals held that the respondent's 1990 petit larceny, a Class A misdemeanor with a maximum of one year imprisonment under New York law, constitutes an aggravated felony. 
"This case requires us to determine whether a misdemeanor can be an "aggravated felony" under a provision of federal law even if it is not, technically speaking, a felony at all. The particular question before us is whether petit larceny, a class A misdemeanor under New York law that carries a maximum sentence of one year, can subject a federal defendant to the extreme sanctions imposed by the "aggravated felon" classification. Despite our misgivings that, in pursuit of a clearly defined legislative goal (to severely punish unlawful reentry into this country), a carelessly drafted piece of legislation has improvidently, if not inadvertently, broken the historic line of division between felonies and misdemeanors, we conclude that Congress was sufficiently clear in its intent to include certain crimes with one-year sentences in the definition of "aggravated felony"..."  —Becker, Chief Judge, U.S. Court of Appeals for the Third Circuit
In the Matter of Crammond, 23 I&N Dec. 179 (BIA 2001), the respondent's California offense for sexual abuse of a minor constitutes an aggravated felony despite the fact that the respondent's conviction was reduced by the court to a misdemeanor punishable by no more than 1 year.
In _ Lopez v. Gonzales_, 549 U.S. 47 (2006), the Supreme Court ruled that because immigration law is under the control of the federal government, the definitions of any terms on the aggravated felony list comes from federal law, not state law. This would mean that by applying the federal law both of the above decisions should and must be oveturned because under federal law a crime must be punishable by imprisonment for a term "exceeding" one year in order to be considered an aggravated felony, otherwise it is cruel and unusual punishment under the Eighth Amendment to the United States Constitution.
In 18 U.S.C. § 921, Congress explains that the term " crime punishable by imprisonment for a term exceeding one year does not include: (A) any Federal or State offenses pertaining to antitrust violations, unfair trade practices, restraints of trade, or other similar offenses relating to the regulation of business practices, or (B) any State offense classified by the laws of the State as a misdemeanor and punishable by a term of imprisonment of two years or less." This means that any state misdemeanor punishable by up to 2 years imprisonment does not qualify an aggravated felony.
In _ Leocal v. Ashcroft, 543 U.S. 1 (2004), the Court ruled that DUI is not an aggravated felony if the DUI statute that defines the offense does not contain _a mens rea element or otherwise allows a conviction for merely negligent conduct.
An alien convicted of an aggravated felony may not:
At the same time, aliens convicted of aggravated felonies are automatically deported through expedited procedures intended to ensure that the deportation occurs as soon as the alien is released from prison after serving the sentence imposed for the underlying crime. These deportation orders are not subject to review by the federal courts, although federal courts have ruled that they may determine which crimes constitute aggravated felonies.
IIRIRA required that aliens convicted of aggravated felonies must be detained while awaiting removal, resulting in the detention of far more aliens than before the Act took effect. In _ Demore v. Kim_, 538 U.S. 510 (2003), the Court ruled that the mandatory detention provision of IIRIRA was constitutional.
The definition of aggravated felony has significantly expanded since its inception in 1988. A series of amendments have expanded its reach to the point that an aggravated felony need not aggravated, nor a felony, to trigger the consequences of such a conviction.
A related use of the term "aggravated felony" comes in the context of the definition of the crime of illegal reentry into the United States following deportation, 8 U.S.C. § 1326, and the corresponding sentencing enhancement provided by the Federal Sentencing Guidelines. It is a crime for an alien to enter or be found in the United States after that alien has been deported. The maximum sentence for this crime is 2 years; however, if that deportation follows a conviction for an aggravated felony, the maximum sentence increases to 20 years.
Furthermore, the guideline that corresponds to this crime typically doubles or triples the sentence the alien would otherwise have received if the deportation follows conviction for an aggravated felony. In _ Almendarez-Torres v. United States_, 523 U.S. 224 (1998), the Supreme Court held that this increased maximum sentence did not violate the Sixth Amendment.