Terzopoulos was born in the village of Makrygialos in northern Greece, the mythical birthplace of Euripides. He is a highly acclaimed director specializing in ancient drama. In 1982, he founded Attis in Athens, one of the most original experimental theatre companies in Greece. He also founded the Theatre Olympics and was artistic director of its first edition in Delphi (1995), as well as the following editions in Shizuoka (1999), Moscow (2001), Istanbul (2006), and Manipur (2008). Since 1993, he also has served as the Chairman of the International Committee of the Theatre Olympics. In 2008 he coordinated the cultural programme of the Olympic Games in Beijing.

In 1985, Terzopoulos initiated the International Meeting of Ancient Drama in Delphi. Some of its participants were: Heiner Müller, Tadashi Suzuki, Robert Wilson, Andrei Serban, Wole Soyinka, Min Tanaka, Andrzej Wajda. Terzopoulos was the artistic director of this festival until 1988. The festival was reactivated in 2005 and 2006. In 1990, he founded the International Institute of the Mediterranean Theatre, currently comprising of 22 countries. The Institute runs an international festival called Violence and Peace in the Mediterranean Theatre, seminars on theatrical education, symposia, and other theatre related events.

Terzopoulos admits that he was brought up in the Brechtian school: he studied Brecht’s legacy while working with the Berliner Ensemble (1972-1976) under the supervision of Heiner Müller, a German dramatist and director who eventually shaped Terzopoulos’ interest in Shakespeare and ancient Greek theatre.

At the Attis Theatre, Terzopoulos stages ancient dramas while being inspired by the works of Beckett, Shakespeare and Müller. He also leads workshops and directs as a guest at other Eastern and Western theatres. In the words of his mentor, Müller: “In Terzopoulos' theatre, myth is not fairytale, it is condensed experience; the process of rehearsal is not the performance of a dramatic concept, it is an adventure on a journey to the landscape of memory, a search for the lost keys of unity between body and speech, the word as natural entity.”

Several of Terzopoulos’ performances have won recognition at international festivals, including The Bacchae and Medea after Euripides, Persians after Aeschylus, and Oedipus Rex after Sophocles. In 2005 , brought AJAX the madness after Sophocles to Poland as part of the 10^th Theatre Confrontations in Lublin.