From 1438 to 1533 , the Incas used conquest and peaceful assimilation to gain a large portion of western South America , that centered on the Andean mountain ranges , and included large parts of modern Ecuador , Peru , Bolivia , Argentina , and Chile . From 1438 to 1533 , the Incas used a variety of methods , from conquest to peaceful assimilation , to incorporate a large portion of western South America , centered on the Andean mountain ranges , including large parts of modern Ecuador , Peru , western and south central Bolivia , northwest Argentina , north and north-central Chile , and southern Colombia into a state comparable to the historical empires of the Old World .