Source: 2003 Farmers and their languages: the first expansions (by Jared Diamond and Peter Bellwood). Science 300:597-603.
Dravidian. "Food production reached South India at about 3000 BC, partly through the spread of Fertile Crescent and Sahel domesticates via the Indus Valley and the north-western Deccan, and partly through a simultaneous spread of rice cultivation from South-east Asia with speakers of Austro-Asiatic (Mundaic) languages. In addition to these undoubted spreads of crops into India from elsewhere, Fuller (68) has recently argued for primarily (independent) origins of rice, millet, and grain domestication in the Ganges Valley and South India. The Dravidian language family is concentrated in South India, with one distinctive outlier (Brahui) far to the northwest in Pakistan, and perhaps an even more distinctive extinct outlier (Elamite) much further to the northwest in southwest Iran (Elamite's relation to Dravidian languages is debated (y69). Either Dravidian languages are the original languages of much of the Indian subcontinent or they arose to the west and spread at about 3000 BC with Fertile Crescent domesticates into the Indian subcontinent, subsequently becoming extinct in their homeland. If the latter interpretation were correct, then one would have to assume either clinal gene dilution or else language shift to explain why South Indians today are phonotypically and genetically so unlike people of the Fertile Crescent. Thus, for South Asian early agriculture, both the archaeological and linguistic records remain equivocal."
Indo-European. "We have saved for last the most intensively studied, yet still the most recalcitrant, problem of historical linguistics: the origin of the Indo-European language family, distributed before 1492 AD from Ireland east to the Indian subcontinent...Indo-European language family contains only 144 languages divided among 11 markedly distinct branches. These and other facts suggest that the task of reconstructing Indo-European origins is complicated by massive extinctions of Indo-European languages in the past, resulting from expansions of a few highly successful subgroups (Germanic, Romance, Slavic, and Indo-Iranian). The two main competing hypotheses of Indo-European origins both face severee difficulties. One hypothesis views Proto-Indo-European as having been spoken in the steppes north of the Black Sea by horse-riding nomadic pastoralists, whose supposed domestication of the horse and invention of the wheel around 4000 BC enabled them to expand militarily (74-76). But objections include that horse domestication and riding may not have begun until thousands of years later (77), that it is hard to understand (perhaps even inconceivable) how steppe pastoralists could have imposed their language on so much of Europe west of the steppes (78); and that even linguists who reject glottochronology agree that Indo-European languages (including Anatolian) are so different from one another that their divergence probably began before 4000 BC (31). The other hypothesis, based on the recognition that the extinct Anatolian languages (inclluding Hittite and Luvian, the probable language of Troy) represent the most distinctive branch and hence the earliest documented branch and hence the earliest documented branching in the family tree, views Proto-Indo-European (or, more strictly speaking, Proto-Indo-Hittite) as a language of Neolithic Anatolian farmers who carried Fertile Crescent domesticates west into Europe, east to the Indus Valley, and north and then east across the Central Asian steppes beginning around 7000 to 6000 BC (32, 78-80). But objections include that the reconstructed Proto-Indo-European lexicon has a strong bias towards domesticated animals rather than crops (81,82) and that reconstructed Proto-Indo-European words relating to wheels and wheeled vehicles suggest (some would say 'prove') late Indo-European origins around the time of the invention of the wheel (~4000 BC)(76). Even we two authors of this paper have differeing views on this issue...
"We also need more studies of languages themselves. Hundreds of historically important languages remain poorly described, efforts to trace so-called deep language relationships (i.e., relations between languages that diverged long ago) remain highly controversial, and relationships of New World languages are especially controversial (43, 86, 87), due in part to the scale of loss and replacement since 1500. Fortunately, linguists are today concerned with modeling the formation of linguistic diversity in time and through space (88), and this is a development to be applauded." http://arts.anu.edu.au/aanda/people/staff/pdfs/bellwood2003.pdf