What defines the "city"?

My apologies if there'd happen to be a discussion, on this matter already. There are a lot of threads in this forum and I can't check all pages.

It's a subject I've been pondering a lot about lately. What makes settlement a "city" and how do you decide what the boundaries of that city are? And how do you decide what the "urban" and "metropolitan" areas are?
I think it's particularly difficult in my home country (Belgium) to set boundaries for cities, because of the population density and the chaotic spacial organization. You often see population centers connected to each other via build-up areas along the main roads. Another problem is that a lot of smaller cities and towns have a long and distinct history, so when they turn into de facto suburbs or satellite cities, they're often not seen that way.

I hope we can have an interesting discussion on the matter.>