Gmail messages seen on iPhone do not appear in Mail App
Double check to make sure you are using IMAP as your incoming mail server request on both your device and your computer.

If those are set correctly, make sure you have the latest OS X updates... I had some issues with missing mail or just mail that took forever to sync down to my computer when I first got Mavericks. I am currently receiving all of my mail now.

Lastly, I know this is stupid, because a lot of people say to do this for everything. But go ahead and restart your computer, some applications will "clog up" with system processes or they will just stop doing some processes all together. A reboot will allow for all caches to be cleared and processes to start from the beginning as normal.