I would like to start looking into Angular or React, but I'm having a hard time at the minute figuring out where they fit in?
I currently build all our sites using PHP based Expression Engine or Craft CMS. Is it possible to use Angular or React with these? Would I be correct in thinking they act as the whole front-end?
So for example, would I use EE/Craft to just create the API's to fetch/post data, and then Angular/React would generate the pages using the data from these calls?
That is exactly what I would do. I am not overly familiar with the CMS frameworks you are using, but do have a good bit of experience with CMS development. Typically I leverage the provided APIs to bring the data to the presentation layer, and then use a JavaScript framework such as Angular to create my UI.
This approach will work great if you can get away with not using any of the CMS server controls, and perform all data operations through API calls.