Hananel ben Chushi'el was born in Kairouan, Tunisia, at the beginning of the 11th century. His father, Chushi'el ben Elhanan, was one of the four rabbis, who, according to legend, was abducted by pirates and landed in Tunisia, where he founded an academy. Ben Chushi'el followed his father as head of the academy.
Ben Chushi'el wrote a tremendous commentary on the Talmud, focusing on the halachic implications of the text. He relied greatly on the responsa and dicta of the geonim, especally the Hai Gaon. However, there were numerous occasions in his commentary when he disagreed with the Babylonian legal positions and provided others, many appearing to come from Jewish Italian traditions. Unfortunatly, only a fraction of his works have survived.
Ben Chushi'el gave translations and explanations for many Greek and Arabic terms and words which appear in the Talmud. His explanations were accepted by Nathan ben Yechiel Anav in his famous lexicon of Talmudic terms.
In his explication of Talmudic legal decisions, Ben Chushi'el was the first to rely largely on the Jerusalem Talmud and on halachic midrash collections.
Ben Chushi'el's commentary and his style greatly influenced Isaac Alfasi, who used several of Ben Chushi'el's decisions in his own commentary. Those decisions later influenced Joseph ibn Migashand RaMBAM.
The Tosafists in Germany and France also accepted Ben Chushi'el's decisions and frequently quoted him.
Sources: Gates to Jewish Heritage