BIRMINGHAM, Ala. (AP) — Monday’s Supreme Court ruling overturning key provisions of Arizona’s illegal-immigration law opens the door for courts to strike down similar measures in states that have tried to make it a crime for illegal immigrants to live and work in the U.S.

Supporters of immigration crackdowns, however, say the ruling also gives states a critical role in enforcing federal law by allowing local authorities to check the immigration status of those suspected of being in the country illegally.