Abaye, whose name was Nachmani, was one of the great Babylonian Amoraim of the fourth generation. Born around the end of the third century as the only son of Kaylil, he lost his father before he was born and his mother at his birth, and was raised by his uncle Rabbah bar Nachmani. He was a Kohen, descended from Eli.

His teachers were Rabbah bar Nachmani and Rav Yosef, and he remained with them all their lives. The Talmud relates that he would rise as soon as he saw the ear of Rav Yosef's donkey approaching. He took care to stay connected with the sages of the Land of Israel, and thus brought teachings of Rabbi Yochanan into the Babylonian Talmud. After the death of Rav Yosef he was chosen to head the academy of Pumbedita, which he led until his death; he also served as a judge.

His debates with his colleague Rava, the "Havayot of Abaye and Rava", touch on nearly every subject in the Talmud and became the very symbol of Talmudic dialectic. In their disputes the halacha follows Rava except in six cases.

Modest and upright, he spent most of his life in poverty, supporting himself by farming. He was known as a man of peace, devoted to acts of kindness and respected by all; one of his maxims urges gentleness in speech and the calming of anger. Although Eli's descendants were destined to die young, he lived about sixty years, by the merit of Torah and acts of kindness. His son, Rav Bivi bar Abaye, was also an amora.

He died in the 330s (337, 338 or 339 according to different sources). According to Rabbi Chaim Vital, he is buried in a cave in the village of Yavnit in the Galilee, alongside Rava and Rav Dimi of Nehardea; local residents established a joint hillula there for Abaye and Rava.