In the Mahabharata, Satyavati was the daughter of a fisherman on the River Ganges. She was extraordinarily beautiful, but she had a horrible odor of fish that would not go away.
The sage Parasara seduced Satyavati as she was fishing from her boat in the river. In appreciation and gratitude, he changed her horrible fishy smell into the fragrance of flowers. As seemed to be the usual practice for seducers of teenage girls in the Mahabharata, Parasara magically restored the girl's virginity. Vyasa is born of their union.
King Santanu falls deeply in love with Satyavati, and his son Bhima enables him to marry the fisher girl.
Santanu and Satyavati had two sons, Citraganda and Vicitravirya. Citraganda dies in battle.
Vicitravirya ascends to the throne. Bhima gets two wives for him, Ambika and Ambalika. When Vicitravirya dies, Queen Satyavati asks Bhima to marry them. But he refuses. Vyasa, who you will recall is Satyavati's son, does the honors. So, Dhritarastra and Pandu, who both become king, are actually Satyavati's grandchildren and not Bharatas by blood.