According to mobile security firm Trust Digital, you're at a real risk of falling prey to an SMS attack while you sleep. Dubbed the "Midnight Raid Attack," because it's mostly run at night, a hacker who has the right toolkits and know-how could send a malicious text message to your phone capable of firing up the web browser and navigating to a harmful website. Once there, the site downloads a dirty executable to your phone intended to steal your private data, said Trust Digital.
"This is a completely real threat," said Phillippe Winthrop, a director in the global wireless practice at Strategy Analytics. "We will see these attacks. It's a matter of time."
Another type of attack has a hacker sending a malicious SMS 'control message' over the GSM network to a victim's phone using a WiFi network, like you might be using at a coffee shop. The attack turns off SSL on the victim's phone, allowing the hacker to sniff your exposed traffic and steal your email credentials.
Trust Digital posted a pair of YouTube videos demonstrating the above attacks, which you can view here and here.