When people call in to radio stations, are the calls broadcast live?

It seems the DJs or whatever are having perfectly normal conversations with the people who call in. I've never called in myself, so I couldn't tell whether I was hearing what those people were saying at the exact same time they were speaking. But if it's live, couldn't it potentially cause problems? Since the people calling in could easily use profanity at the DJ and say a lot of mean things.