The Indus Valley Civilization is the indigenous civilization in the region of India, Pakistan, and parts of Afghanistan and Iran. It traded with Ancient Egypt, Sumeria, Greece, and Rome. For its time, it was the largest ancient civilization, and it was highly impressive (they had uniform brick buildings, perpendicular grid streets, covered sewers, a base-10 system of standardized weights, etc. : http://en.wikipedia.org/wiki/Indus_Valley_Civilization#Matur...) The IVC collapsed before Greece and Rome reached their peaks, but in the absence of more research, we can only surmise its legacy (e.g., Indian sarees, white waistcloths and sandals may have been mimicked as togas). I think more research needs to be done to flesh out all of the loose ends of inquiry, and lots of interesting research is happening currently. I'm sure more facts will continue to emerge about the IVC that shift our understanding of the world's history.

The prevailing theory is that the IVC bequeathed culture (religion, customs, knowledge, architecture, etc.) to all parts of the region. It is believed that the IVC inhabitants spread east and southwards to fill all parts of India. The IVC collapsed (1900 BCE), and around 1000 years afterwards (1000 BCE), a branch of proto-Indo European language speakers is believed to have moved south from the Caucuses into Iran/India. The language they spoke (Sanskrit) is believed to have taken on influences by the indigenous language taken hold in the northern parts of India, but considering their much fewer numbers and nomadic lifestyle at the time of their arrival, their genetic contribution is thought to be minimal. After the British colonial scholar Robert Caldwell, a scholar in Sanskrit, noticed the difference between the languages of north India (Indo-European > Sanskrit derived) and southern India (a distinct language family, of which Tamil has the least influence of Sanskrit), he used the term "Aryan" to describe the northern languages and "Dravidian" to describe the southern languages. (side note: Caldwell was opposed to and upset with attempts by people to project the terms Aryan and Dravidian for the purposes of racism and hegemony; he personally believed in the opposite) It is also believed that at the time of arrival of the Sanskrit speakers to India from the north, the existing indigenous culture (i.e., of the people from IVC) heavily influenced that of the arriving people. Among the first writings in Sanskrit (Veda scriptures), the earliest shows the most indigenous influence (e.g., water-based imagery), and the later Veda writings show a diminishing influence towards a more Sanskritic one (e.g., fire-based imagery). In light of all of this, scholars say that pretty much the only evidence we have that "Aryans", as a distinct group, existed is their language.

It is widely believed that the language of the IVC is most closely related to Dravidian languages, and the best attempts to decipher their writing comes from using Tamil as the starting point. An interesting, recent paper from last year puts forward a very compelling advancement in interpreting the script, and in the process, it further fleshes out the relationship between IVC, the culture of Indian peoples, Sanskrit writings and Dravidian languages:

http://harappa.drupalgardens.com/content/indus-fish-swam-gre...

Because of Caldwell's linguistic analysis and the convenient role it played in political maneuvering for accruing power in British colonial India (by the British, and by people in India regionally and caste-wise), the division along "Aryan"/"Dravidian" lines became seen as a racial one. (If there is a difference genetically today, it may be from the occasional invasion by empires from the Middle East in the north of India over the millennia, from which the south was largely insulated by the Deccan Plateau). As the idea of this racial divide survives while India is now divided into states based on language (and the southern states are a minority), and given the roughly 90/10 split of Hindus and Muslims, chauvinism along religious, geographic, and linguistic lines has gradually coalesced. It's to the point where some Indians want to portray the IVC as Sanskritic/Aryan (and Sanskrit-speakers as the originators of Hinduism because the oldest known Hindu writings are in Sanskrit), even if they have to blatantly distort facts:
http://safarmer.com/frontline/horseplay.pdf
But more commonly, you'll find resistance among such people from accepting a proto-Dravidian language hypothesis of the IVC in favor of interpreting the IVC in a Sanskritic light:
http://www.sanskrit.org/www/Hindu%20Primer/induscivilization...