Like archaeologists, linguists and geneticists too use the data and methods of their disciplines to open up their own windows onto our past. These disparate visions of human prehistory cry out to be reconciled into a coherent holistic scenario, yet progress has long been frustrated by interdisciplinary disputes and misunderstandings (not least about Indo-European). In this article, a comparative-historical linguist sets out, to his intended audience of archaeologists, the core principles and methods of his discipline that are of relevance to theirs. They are first exemplified for the better-known languages of Europe, before being put into practice in a lesser-known case-study. This turns to the New World, setting its greatest indigenous ‘Empire’, that of the Incas, alongside its greatest surviving language family today, Quechua. Most Andean archaeologists assume a straightforward association between these two. The linguistic evidence, however, exposes this as nothing but a popular myth, and writes instead a wholly new script for the prehistory of the Andes — which now awaits an archaeological story to match.