Crime and illegal immigration are at decades-long lows, says Barack Obama

In his keynote speech on the third night of the Democratic convention, President Barack Obama devoted time to attacking Republican nominee Donald Trump, saying that the candidate promising to "Make America Great Again" is living in a country that is already great.

"Ronald Reagan called America 'a shining city on a hill,' " Obama said. "Donald Trump calls it 'a divided crime scene' that only he can fix. It doesn’t matter to him that illegal immigration and the crime rate are as low as they’ve been in decades, because he’s not offering any real solutions to those issues. He’s just offering slogans, and he’s offering fear. He’s betting that if he scares enough people, he might score just enough votes to win this election."

Trump did, in fact, call the United States "a divided crime scene" in a tweet. But for this fact-check, we're going to focus on Obama's claim about illegal immigration and crime....
http://www.politifact.com/truth-o-meter/statements/2016/jul/28/barack-obama/crime-and-illegal-immigration-are-decades-long-low/