In German restaurants (at least the less fancy ones) the waiter usually brings you the check and immediately collects the money.
In other European countries (e.g. France, Italy, Belgium), the waiter brings you the check and leaves.
I've always managed to pay my bill in some way, but never understood what the intended follow-up is.
Suppose you want to pay in cash (otherwise it's simple) and you don't need any change:
Do you lay the money on the table and leave? Or do you lay the money on the table and wait?
If (as common) the check is in a book, do you place the money on or in the book?
If the answer to 1. is "wait" and the answer to 2. is "in", the waiter can't see if you've put the cash in. Does he come back after some time or does he wait for a signal?