Do Nahuatl and Quechua still live, and what words did they give the world?

Yes, both languages are alive. Nahuatl, the language of the Aztecs, is spoken in varieties by about 1.7 million Nahuas, mostly in central Mexico. Quechua, the main language of the Inca Empire, is the most widely spoken pre-Columbian language family in the Americas, with an estimated 8 to 10 million speakers in 2004 and just under 7 million in recent census data.

They also live in your own vocabulary. English has absorbed Nahuatl words including avocado, chili, chocolate, coyote and tomato, and the names of Mexico, Guatemala and Nicaragua derive from Nahuatl. Quechua words that reached English via Spanish include coca, condor, jerky, llama, poncho, puma, quinine and quinoa.

That they survived is not a given. Nahuatl was even promoted by the Spanish Crown for a while: in 1570 King Philip II decreed it the official language of New Spain's colonies to help communication. But in 1696 Charles II banned the use of any language other than Spanish throughout the empire. Quechua was tolerated until the 1780s.

Today the picture is mixed. Nahuatl was spoken by over 5% of Mexicans in 1895 and by 1.49% in 2000. Quechua lost prestige, but Peru recognised it as an official language in 1975, Ecuador in 2006 and Bolivia in 2009, and Mexico's 2003 law gives Nahuatl and 63 other Indigenous languages the same status as Spanish in the regions where they are spoken.