In this talk, I will summarize the results of two papers, Narasimhan, Patterson et al. Science 2019 and Shinde, Narasimhan et al. Cell, 2019, as well as some unpublished data which together report ancient DNA data from 524 individuals from across Central and South Asia, including importantly the first genomic data from an individual from the Indus Valley Civilization. I will briefly overview how the major cultural transformations of farming, pastoralism, and shifts in the distribution of languages in Eurasia were accompanied by movement of people and were possibly related to the spread of Indo-European languages through into the sub-continents of India and Europe. In particular, and in relation to the symposium, I will discuss several possibilities for the spread of Indo-European languages within India and what genetics can say or cannot say yet, about the timing of these events.