If you have made a substitution in either normal mode :s/A/B/g (the current line) or visual mode :'<,>'s/A/B/g (lines included in the current selection) and you want to repeat that last substitution, you can:
Move to another line (normal mode) and simply press &, or if you like, :-&-<CR> (looks like :&), to affect the current line without highlighting, or
Highlight a range (visual mode) and press :-&-<CR> (looks like :'<,'>&) to affect the range of lines in the selection.
With my limited knowledge of Vim, this solves several problems. For one, the last visual substitution :'<,'>s/A/B/g is available as the last command (:-<UP>) from both normal and visual mode, but always produces an error from normal mode. (It still refers to the last selection from visual mode - not to the empty selection at the cursor like I assumed - and my example substitution exhausts every match in one pass.) Meanwhile, the last normal mode substitution starts with :s, not :'<,'>s, so you would need to modify it to use in visual mode. Finally, & is available directly from normal mode and so it accepts repetitions and other alternatives to selections, like 2& for the next two lines, and as user ruohola said, g& for the entire file.
In both versions, pressing : then & works as if you had pressed : and then retyped s/A/B/, so the mode you were in last time is irrelevant and only the current cursor line or selection determines the line(s) to be affected. (Note that the trailing flags like g are cleared too, but come next in this syntax too, as in :&g/: '<,'>&g. This is a mixed blessing in my opinion, as you can/must re-specify flags here, and standalone & doesn't seem to take flags at all. I must be missing something.)
I welcome suggestions and corrections. Most of this comes from experimentation just now so I'm sure there's a lot more to it, but hopefully it helps anyway.