Indigenous civilizations in the Americas were thriving during the Middle Ages while Europe experienced turmoil. The Olmec, Toltec, Maya, Inca, and Aztec empires rose and fell, achieving advanced cultures with complex governments, calendars, mathematics, and architecture. The Aztec Empire was the largest, controlling territory from central Mexico through tribute and religiously-motivated human sacrifice, until it was conquered by the Spanish led by Cortez in 1519.