Introduction
Vishvarupa, "of every form", is the three-headed son of the craftsman-god Tvashtri, made priest (purohita) of the gods, whose death at Indra's hand set off the chain of events leading to the creation of Vritra.
This article follows the Puranic tradition. Where a detail differs between texts, the article says so.
Family
The three heads
Vishvarupa's three heads are described as drinking soma with one, wine with a second and eating food with the third, or as facing the four (or three) directions to see everything, in keeping with his name. Some accounts make him the son of Tvashtri by an Asura mother, which is given as the reason for suspicion that his sympathies lay with the Asuras rather than the gods, whose priest he had been appointed.
Death
Believing Vishvarupa was secretly favouring the Asuras in his priestly duties, Indra killed him, cutting off his three heads. This act, a serious offence against a Brahmin, is one of several sins that trouble Indra in the epics and Puranas.
The creation of Vritra
Enraged at the killing of his son, Tvashtri performed a sacrifice from which Vritra arose, born specifically as an enemy powerful enough to destroy Indra, which set in motion the Vritra myth.