How do I size a UITextView to its content?

This works for both iOS 6.1 and iOS 7:

- (void)textViewDidChange:(UITextView *)textView
{
    CGFloat fixedWidth = textView.frame.size.width;
    CGSize newSize = [textView sizeThatFits:CGSizeMake(fixedWidth, MAXFLOAT)];
    CGRect newFrame = textView.frame;
    newFrame.size = CGSizeMake(fmaxf(newSize.width, fixedWidth), newSize.height);
    textView.frame = newFrame;
}

Or in Swift (Works with Swift 4.1 in iOS 11)

let fixedWidth = textView.frame.size.width
let newSize = textView.sizeThatFits(CGSize(width: fixedWidth, height: CGFloat.greatestFiniteMagnitude))
textView.frame.size = CGSize(width: max(newSize.width, fixedWidth), height: newSize.height)

If you want support for iOS 6.1 then you should also:

textview.scrollEnabled = NO;