Rollback with functions

Greetings!

I have yet not fully understood the magic with transactions in
combination with plpgsql functions.

Assume I have a function

create function foo()
begin
do stuff
....
.... <--- here it fails
....
end

and a call to the function fails (as indicated in the code), will
everything that has been done inside the function be automatically
undone (rollbacked)?

If I had added code for exceptions, like this

create function foo()
begin
begin
do stuff
....
....
....
exception when others then
.... <--- clean up code
end;
end

Then I would need the "clean up code", or else there would be some
changes in the database caused by all the commands that were actually
run before the failure, right?

So is there then any other reason besides having a way to tell exactly
what went wrong (which I understand is a good thing ), to have the
"clean up code"? (you might of course need to have more exception
statements and add exceptions to the clean up code, and so on...