In the last year or so, state governments have taken some of the most high-profile actions on the issue of immigration (especially on the issue of illegal immigration). They have done so in large part because the federal government has been unable to come up with any serious policy to reduce the levels of illegal immigration.
The best-known state action on immigration was the law passed by the state of Arizona. This law gave police officers in Arizona the power to stop people who they suspected of being illegal immigrants. The police could demand identification and detain those who could not prove they are in the US legally. The passage of this law has created a political uproar and has led to a great deal of litigation as well.
Other states and some localities are considering laws similar to the Arizona law and/or are taking other steps to curb immigration (such as ending food stamp eligibility for legal immigrants, which my state, Washington, is currently considering).