Last week, the Supreme Court heard oral argument regarding Arizona's SB 1070 - their aggressive immigration law. The federal government argued that the court should strike down part of the law - the "show me your papers" part - that requires state law enforcement officials to stop and ask people of their citizenship status if they suspect that they aren't in the US legally. The law also makes it a crime for undocumented immigrants to work. Several other southern states have modeled immigration laws off of Arizona's.
The reason why Arizona's law is being challenged is because the Constitution's supremacy clause causes federal law trumps state law, so if they conflict, federal law prevails. The court will rule in June, deciding whether or not parts of the Arizona law conflict with federal law. If the court upholds the law, it still might be challenged by arguing that the law discriminates based on race and ethnicity.
Want to learn more about how any state immigration laws might effect you, contact an immigration lawyer.