Since iOS 8 was released in September 2014, Apple has encrypted the local storage of all iPhones. That’s not news, but it’s become newly relevant since the company and the FBI started a very loud, very public fight about the data stored on a particular iPhone.
If you're looking for comprehensive privacy, including protection from law enforcement entities, there’s still a loophole here: iCloud. Apple encourages the use of this service on every iPhone, iPad, and iPod Touch that it sells, and when you do use the service it backs up your device every time you plug it into its power adapter within range of a known Wi-Fi network. iCloud backups are comprehensive in a way that Android backups still aren’t, and if you’ve been following the San Bernardino case closely you know that Apple’s own legal process guidelines (PDF) say that the company can hand iMessages, SMS/MMS messages, photos, app data, and voicemail over to law enforcement in the form of an iOS device backup (though some reports claim that Apple wants to strengthen the encryption on iCloud backups, removing its ability to hand the data in them over to law enforcement).