The Aztec nobles had slaves. 

Slaves were not captured people. They were Aztecs. There were only two ways you could become a slave. You could become a slave as punishment for a crime you had committed. You could be voluntarily sold into slavery. These were the only two ways. 

The life of a slave was pretty much like the life of a freeman. Slaves could marry other slaves and even a freewoman. 

Children of slaves were not slaves themselves. You could not be born into slavery in the Aztec world.

It was difficult to get rid of slave once you bought one. If your slave refused to do your bidding, you have to bring your slave to a plaza, and in front of witnesses, prove your slave would not do what they were supposed to do. You could not just do this once. You had to do this three times, using three different acts of refusal. After the third one, you could bring your slave back to the slave market. The slave would then be resold to someone else. A slave had to be sold and resold three times to three different masters before a slave could be sold for sacrifice.

Slaves could buy their freedom. All they needed to do was fine the money to pay their owner what he had paid to buy them.

The Aztecs had another interesting law about slavery. On the way to the slave market, where the slave was about to be sold or resold, if a slave got away and managed to run to the palace without being stopped, that slave was immediately free. The only person who could chase that slave was the master’s son. If anyone interfered with the race, that person became a slave.