I have taken a lot of photos on my iPhone. But when I connect it to my Mac, the photos do not show up in Preview. I can see the photos on the iPhone, but they are simply not recognised when I plug the iPhone to the Mac - any ideas?
The photos on iPhone doesn't directly show up in Preview.app on your Mac after connecting. You will need to copy (via import or sync) them to your Mac to be able to see them in Preview.app.
After connecting your iPhone to your Mac, launch Image Capture.app. You can find the app in Other folder in Launchpad, or simply search for it via Spotlight.
Once the app is launched, your iPhone is unlocked and both the iPhone and Mac have trusted each other, you should be able to see all the photos and videos in the Image Capture.app window.
Simply select, drag and drop the photos from within Image Capture app onto a folder in Finder to copy them to your Mac.