Civ V won't let me destroy other cities

Question

I'm at war with a country. I destroyed a city (it has 0 health) but it isn't letting me annex/create a puppet city out of it. It keeps saying that it's still owned by the Aztecs. Every turn it is able to harm my units and regains health.

If I attack the city after it's out of health, the attack animation plays but the red -20 health thing doesn't show, and their health bar doesn't go down.

The city I'm destroying isn't their capital, and I haven't attacked any other cities.

The civ I'm trying to destroy is the Aztecs. I have the brave new world DLC.

Answer 1

You are unable to take a city via a normal ranged unit attack command. You will need a unit that can actually invade the city itself to gain control over it. Some say you can use the move command if a cities health is low enough but I haven't actually ever tried that. The best way I know of is to use a melee unit to invade the city after you have its health down low enough.

Answer 2

You aren't playing "One City Challenge" are you? Found in the advanced setup menu, this challenge only allows you to own one city the entire game.