Being a celebrity has its many perks, but it also has a lot of downfalls. The more influence you have in the public eye, for instance, the less privacy you're allowed to have. Fans, news sites, and even people who don't like you will try to know where you are at all times.
Some celebs will take to disguises, like hoodies and sunglasses, to keep their fans away. Usually, though, eagle-eyed fans and news outlets can spot a celebrity no matter how many layers they're wearing. Take Justin Bieber, for instance. He went all out on a wig while in Tokyo, Japan, and still got spotted out and about.