Use WebDAV to transfer files between iPhone / iPad and Mac computers.
Remote Drive - WebDAV
On your iPhone / iPad

Switch to iPhone / iPad view
From the main menu, switch to local storage view.

Tap ... menu button
Tap button in the top right corner of the screen to display context menu.

Enable WebDAV
Select "WebDAV server" from the menu to enable WebDAV on your device. Keep the app in the foreground while you using WebDAV to transfer files.
Tap "Stop" when you finished using it.
Tap "Stop" when you finished using it.
On your Mac

Open Finder menu
Switch to Finder, and open "Go" menu item, and select "Contact to Server..."

Enter iPhone address
Enter the address shown on your iPhone / iPad in the dialog, including "http://"

Connect
Click "Connect" in the dialog to allow your Mac to connect to your iPhone / iPad.

Authenticate
Enter user name and password as shown on your iPhone / iPad and click "Connect".

Browse files
From sidebar menu select your iPhone / iPad. Now you can transfer files to and from your iPhone / iPad as you would with any other network drive.
Once you finish, click on "Eject" button and tap "Stop" button on your iPhone / iPad device.
Once you finish, click on "Eject" button and tap "Stop" button on your iPhone / iPad device.