He is the author of six books, among which The Faces of Justice and Evidence Law Adrift were translated into several languages. He has published more than 100 articles in professional journals of numerous countries.
He received his basic law degree at the University of Zagreb in his native Croatia. He then studied at the Academy of International Law at The Hague, and the Comparative Law Faculty in Luxembourg. He earned his Ph.D. at the University of Ljubljana (Slovenia). Following time spent practicing in the courts of former Yugoslavia, he began his teaching career at the University of Zagreb Law School, rising quickly to the rank of full professor, and briefly serving as Acting Dean. In 1971, he left his native land, and accepted a tenured position at the University of Pennsylvania Law School. Since 1976, he has been on the faculty of Yale Law School.
Damaška is a fellow of the American Academy of Arts and Sciences, a member of the International Academy of Comparative Law, the Croatian Academy of Arts and Sciences, and the American Society of Comparative Law. In 1978-79, he was fellow of the National Endowment for the Humanities. He is also holder of several honorary degrees.
He was keynote speaker and general reporter at many international congresses. Five symposia were organized about his work: Bielefeld (Germany) in 1987; Siena (Italy) in 1988; San Francisco in 1998; Zagreb (Croatia) in 2006; and New Haven in 2008. From 1990 to 1995, he served on the Advisory Board of the Central and East European Legal Initiative of ABA. Since 1995, he has periodically advised the Croatian government in its relations with the International War Crimes Tribunal for the Former Yugoslavia, and the International Court of Justice in The Hague.
In 2005, he was appointed Amicus Curiae of the International War Crimes Tribunal for the Former Yugoslavia in the matter of transferring cases to domestic courts. In 2009, he was presented the lifetime achievement award by the American Society of Comparative Law. In 2014, he was awarded the Life Achievement award by Jadranko Crnic Foundation, Croatia. He does counseling work on foreign law problems for law firms in New York, Los Angeles, and Washington.
In 2010 he was appointed special adviser to the Prime Minister of Croatia, and agent of the Republic of Croatia before the International Court of Justice, heading a team of Croatian and English lawyers in the case of Croatia v. Serbia.