Have you recently updated your phone or reset it? If so, sometimes you will have to reinstall all the drivers for the phone to the PC... USB debugging, MTP, PTP, fastboot and etc... Before the PC recognizes the device again.
The pictures on the device are stored on the internal memory in either -
/SD card/DCIM/ thumbnails/ and/or also in /SD card/DCIM/camera.
To move files from one folder to another folder or to even create a new folder and to view these device directories you will need to use an app like "Root Browser" and you may need root to be able to edit and or read and write to the directories.
Also as amarie82 said, you can also use a cloud storage based app like Dropbox, OneDrive or Google+ to automatically sync and backup you pics. Then they are easily viewable and manageable through these apps.