The Indus gives its name to India, to Hinduism and to the Sindhi people, by a chain of borrowings: the Sanskrit Sindhu became the Persian Hindu, which the Greeks rendered as Indos, and each of those forms then became the name for a country, a people or a faith. The word Hindu therefore began as a geographical term for people living beyond a river, and only much later became the name of a religion.
The Rigveda names the river and its tributaries repeatedly, and the hymn addressed to the rivers praises the Sindhu as loudest and swiftest among them, running ahead of the others like a bull. That hymn is one of the clearest pieces of internal evidence for where the Vedic hymns were composed, since the rivers it lists run from the northwest in a sequence that can be followed on a map.
Long before those hymns, the same plain carried the Harappan cities. Mohenjo-daro stood on the Indus itself, and the civilisation's dependence on the river's flood cycle is generally accepted as central to both its rise and its decline, although the mechanism of the decline is argued.
Downstream, in Sindh, the river's saint is Jhulelal, revered by Hindu Sindhis as an incarnation associated with the water and honoured at shrines that Muslims have also frequented, which is a common pattern along the lower river.