Quechuan is the most widely spoken indigenous language family in the Americas, with something near eight million speakers in Peru, Bolivia, Ecuador and neighbouring countries. Whether it is one language or forty depends on the criterion used, since it forms a chain of varieties in which neighbours understand each other and the ends do not. Its history involves two separate imperial expansions.
The Inca state adopted a Quechuan variety as the language of administration and spread it deliberately across the territory it controlled, which was already an expansion beyond the family's homeland. Then the Spanish, arriving in the sixteenth century, kept it: colonial administrators and above all missionary orders used Quechua as a general language for governing and evangelising, produced grammars and catechisms in it, and thereby carried it into regions the Inca had never reached.
The homeland itself is not Cusco, despite the Inca association, but the central Peruvian coast and adjacent highlands, where the deepest internal divisions lie. Separating the language from the state that made it famous is the first thing to get right about it. Aymara, spoken alongside Quechua around Lake Titicaca, is a separate family and not a Quechuan language, though the two have been in contact so long and borrowed so heavily that a proposed Quechumaran grouping has been argued for and never established. The atlas keeps them apart, which is the majority position.