This answer is great for seeing a visual diff between two files that are checked into git: How do I view 'git diff' output with a visual diff program?
Howev
Try "difftool" (assuming you have diff tools setup) - see https://www.kernel.org/pub/software/scm/git/docs/git-difftool.html
I find name status good for the summary but difftool will iterate the changes (and the -d option gives you the directory view), e.g.
$ git difftool their-branch my-branch
Viewing: 'file1.txt'
Launch 'bc3' [Y/n]:
...
Or as @rsilva4 mentioned with -d and default to your current branch it is just - e.g. compare to master:
$ git difftool -d master..
...and yes - there are many variations - https://www.kernel.org/pub/software/scm/git/docs/git-reset.html