What have the Greeks ever done for us?

Some things were built to last. In the beginning there was poetry, both epic and lyric. Eventually came festivals where poets competed for prizes during the celebration of Dionysus, the zaniest god. The poetry split into spoken verse and sung chorus, and so tragedy was born.

Myths were plundered for plot. Masks allowed for the portrayal of legendary characters. Rules and conventions cohered: a high-status individual is brought low by a tragic flaw, a messenger describes off-stage calamities, everything may or may not end horribly. Venues were built, special effects created, literary criticism born, and the whole enterprise was paid for by a complicated public-private partnership. But, apart from that, what have the Greeks ever done for us?

From doomed Oedipus to scorned Medea, every protagonist of a Greek classic knows (or at least ought to know) that it’s impossible to escape your origins. Something similar seems to happen with dramatists, from Shakespeare to Racine, Eugene O’Neill to Edward Albee, Frank McGuinness to Charles Mee, who return to the classics ceaselessly, fascinated with the source.

The classics are here again at this year's Tiger Dublin Fringe, transformed but familiar. As a disguised, vengeful Orestes might say to his sister Electra, just don't call it a comeback.

In rehearsals for The Rest Is Action, the latest show from the Company, its director, José Miguel Jiménez, and his cast seem to be teasing out the bloody logic of their loose adaptation of The Oresteia. "I die, she dies, you kill him," Rob McDermott says. "So who's going to be here to kill you?"

The Company's previous works include an adaptation of Jorge Luis Borges and James Joyce, always less occupied with faithfully transplanting the text to the stage than with discovering thoughtful, playful theatrical correspondences. For Ulysses, performed as As You Are Now So Once Were We, they abandoned Leopold Bloom altogether and made a show about four competing perspectives through one day's journey across Dublin.

With The Oresteia, the only extant Greek trilogy, which they consider the foundation of both theatre and democracy, the aim is similar.

"I suppose the main element of The Rest Is Action is the idea of going through certain narratives that are inherited, that are always present, and realising that every attempt to get out of a narrative only results in finding another," says Jiménez. The Greeks had a fatalistic understanding of this: Damned if you do, damned if you don't.

"It's supposed to be, literally, a rehearsal of democracy," Jiménez says. "It's the point at which the transference from mythical era into rational era takes place. The first play [in the trilogy, Agamemnon] is about gods and the inevitability of fate. In the second one [The Libation Bearers], the son tries to resist but still goes through with it. By the third play [The Eumenides, the Trial of Orestes], it's strange on every level. In the end you enter this new order. Now man is in charge."

Former students on Trinity College Dublin’s acting course, the Company had encountered Aeschylus’s plays before. What did they mean to them back then? “Nothing!” says Nyree Yergainharsian, with mock exasperation. “It sounded weird; it looked weird. Nobody knew how to relate to it, so there’s never a chance to fully believe in what’s going on.”

To bridge that distance their riffs around the material are clever and contemporary: what did the house of Atreus neighbours make of it all? How would it have turned out if Orestes was an atheist? But the more philosophical point is about the inescapability of narrative and destiny; that you never leave anything behind, and that has shuddering consequences. "The modern world stems from it," says Brian Bennett, speaking of cyclical chaos and bloodshed, "and people wonder why the modern world is the way it is."

It's a similarly sobering point in the Canadian performer Evan Webber's double bill, Ajax and Little Iliad, both inspired by Sophocles's Trojan War plays. Following the methods of an American-military-supported company, Theatre of War, who use these plays to help returning soldiers work through post-traumatic stress disorder, Webber and Frank Cox-O'Connell stage a beautifully conceived Skype conversation in which one friend challenges another about duty, opening into a consideration of the relationship between art and war.

“From my perspective it’s inspiring and very troubling,” Webber says of Theatre of War’s methods. “I have a hard time seeing the reassurance in the prospect of these traumas being endless. To say that war is natural is to say it’s not changeable.”

Little Iliad neatly problematises this; Ajax is a more vaudevillian take on classic structure, casting the audience as the chorus while the two actors wear goofy togas. "I have no interest in trying to resuscitate these old stories. I'm more interested in an exorcism or a conclusion to telling these things. The fact that these stories are relevant is like a problem to be worked on."

Webber gamely concedes it’s an unlikely aspiration, to reach for one final catharsis that makes Greek theatre obsolete, yet it’s an engaging idea: “To think about how we can change our behaviour.”

That, however, is what we’ve been doing since the first goat was slaughtered at the commencement of Athenian entertainment, in every revisited classic plot, every departure still umbilically connected to its origins, every attempted reinvention of the wheel. However far we get from the ancient Greeks, we keep going back.

The Rest is Action ends today at Project Arts Centre; Ajax and Little Iliad run from Tuesday to Saturday at the Peacock Theatre; fringefest.com