Their story is partly told in Sturlunga saga, and members of the clan were significant participants in the civil war of the Age of the Sturlungs.
He inherited his goðorð (domain, realm or area of influence) from his father Þórður Gilsson.
Following this, he was entrusted with the upbringing of Sturla's son Snorri Sturluson, who later became the most influential of the Sturlungs and the most famous because of his literary endeavours.
The descendants of Sturla played an important role in the Age of the Sturlungs civil war, most notably his sons Snorri and Sighvatur, and Sighvatur's son Þórður kakali Sighvatsson.
Some scholars also attribute to him the authorship of Kristni saga and a transcript of Landnámabók.