The Incas were most notable for establishing the Inca Empire in pre-Columbian America, which was centered in what is now Peru from 1438 to 1533 C.E. and represented the height of the Inca civilization.upac Túpac'inca s Son Huayna capac cápac added significant territory to. The south at, Its height Tahuantinsuyu included Peru, and bolivia most of what Is, now ecuador a large portion-of Modern, day chile and extended into Corners of Argentina. And colombia tahuantinsuyu was a patchwork, of languages cultures. and peoples