The Supreme Court struck down much of the law, but a key portion that requires the police to check the status of someone they suspect is in the U.S. illegally could go forward. From AP:
The decision upholds the "show me your papers" provision for the moment. But it takes the teeth out of it by prohibiting police officers from arresting people on minor immigration charges. Justice Kennedy wrote the opinion for the court that was unanimous on allowing the status check to go forward. The court was divided on striking down the other portions.
From the Washington Post:
The court ruled that Arizona cannot make it a misdemeanor for immigrants to fail to carry identification that says whether they are in the United States legally; cannot make it a crime for undocumented immigrations to apply for a job; and cannot arrest someone based solely on the suspicion that the person is in this country illegally.
*Tom Goldstein of Scotusblog tweets: "On net, the #SB1070 decision is a significant win for Obama Admin. It got almost everything it wanted."