Many hypotheses have been put forward about the affinity of the Indus language, but only two alternatives have had wider support.
Indo-Aryan languages have been spoken in the area once occupied by the Indus civilization and gradually all over North India since at least 1000 B.C. It is natural to assume that they were spoken there even earlier. Speakers of Hindi, Bengali and other Neo-Indo-Aryan languages especially have been prone to interpret the Indus texts as Sanskrit (understood in the broad sense of Old Indo-Aryan), from which their own mother tongues have evolved.
The Sanskrit hypothesis, however, is difficult to reconcile chronologically with the date of the Indus civilization (about the second half of the third millennium B.C.) and antecedent Early Harappan neolithic cultures which were responsible for its creation. Comparison of the Vedic texts with the Avesta and with the West Asian documents relating to the Aryan kings of Mitanni suggests that the Vedic Aryans entered the Indian subcontinent from Northeast Iran and Central Asia in the second millennium B.C.
Moreover, it is abundantly clear that the early Aryans were nomads and that the horse played a dominant role in their culture, as it did in the culture of their Proto-Indo-European-speaking ancestors. The horse is conspicuously absent from the many realistic representations of animals in the art of the Indus civilization. Comprehensive recent bone analyses have yielded the conclusion that the horse was introduced to the subcontinent around the beginning of the second millennium B.C.
Horse-drawn chariots made the Aryan-speaking nomads a superior military force which gradually subdued all of North India. Numerically the early Aryans can have been only a fraction of the Indus population, which is estimated to have been about five million. Obviously these millions of people were not all killed; they were made to acknowledge the Aryan overlordship and to pay taxes. In the course of time and through gradually increasing bilingualism, the earlier population eventually became linguistically assimilated. It is most unlikely that this process of linguistic Aryanization happened without leaving clear marks of the earlier substratum language upon Indo-Aryan.
There are several structural and lexical Dravidisms even in the Rgveda, the earliest preserved text collection, pointing to the presence of Dravidian speakers in Northwest India in the second millennium B.C. The 25 Dravidian languages spoken at present form the second largest linguistic family of South Asia. Until recently, about one quarter of the entire population has spoken Dravidian, while the speakers of Austro-Asiatic, the third largest linguistic family of long standing in South Asia, numbered just a few per cent. The Indus language is likely to have belonged to the North Dravidian sub-branch represented today by the Brahui, spoken in the mountain valleys and plateaus of Afghanistan and Baluchistan, the core area of the Early Harappan neolithic cultures, and by the Kurukh spoken in North India from Nepal and Madhya Pradesh to Orissa, Bengal and Assam.
[Originally published as Parpola, Asko (1988) Religion reflected in the iconic signs of the Indus script: penetrating into long-forgotten picto+graphic messages. Visible Religion 6: pp. 114-135.]