My Canon 70D doesn't always import the pictures when I plug it in to my Apple computer. After plugging it in, sometimes the window pops up to automatically import the pictures and other times it doesn't, nothing happens. I just took pictures of an orchestra concert last night and I can't transfer them to my computer. I've tried to turn the camera off and on and unplug the cable but nothing works.
What software are you trying to use?
Which Apple OS version are you running?
Are you using a USB "hub" or directly connecting the camera's USB cable to a USB port on the Mac?
There is a way to tell the Mac what you want it to do when you attach a camera or card that contains image data. One of the easier methods is to use the Apple "Image Capture" utility which lets you specify which program should be launched if that camera or device is connected. I specifically go through all my cards and cameras and set them to "do nothing" so I can control what gets launched (by default, most Macs will launch the "Photos" app if any camera card or camera is connected.)
You can set it to launch anything... I've configured my Mac to launch Lightroom (just for example.)
With a bit more info, I might be able to offer you more specific instructions.