Update (June 2016): I now try to support touch and mouse input on every resolution, since the device landscape is slowly blurring the lines between what things are and aren’t touch devices. iPad Pros are touch-only with the resolution of a 13″ laptop. Windows laptops now frequently come with touch screens.
Other similar SO answers (see other answer on this question) might have different ways to try to figure out what sort of device the user is using, but none of them are fool-proof. I encourage you to check those answers out if you absolutely need to try to determine the device.
iPhones, for one, ignore the handheld query (Source). And I wouldn’t be surprised if other smartphones do, too, for similar reasons.
The current best way that I use to detect a mobile device is to know its width and use the corresponding media query to catch it. That link there lists some popular ones. A quick Google search would yield you any others you might need, I’m sure.
For more iPhone-specific ones (such as Retina display), check out that first link I posted.