How to make my iphone appear as a device or show up as an icon on my mac?

I'm trying to open some files on my iphone but I can't find it on my laptop. It works fine when I use it on iTunes, however I want to be able to open it as if it were a device. How can I make it appear as a device on my laptop or at least show up as an icon?

No idea which Mac, which OS version. My answer is for MacBook Pro 13" 2013 and OS 10.8.5

For copying files from an iOS device to a Mac, try any of the options below.

In the long run, it is better to use a thumb drive to move files from one computer to another. The phone isn't really designed to be used as a portable drive.