This week, the actor Lia Williams visited a butcher’s shop. There, she learned how to stab a knife through live flesh and ribs: to feel in her arm and hand what it is to cut through a body, through its sinew and muscle and bone, to the death. This is part of her preparation for playing one of the great roles in theatre, Clytemnestra. This powerful, clever, rhetorically able, much wronged and murderous woman appears in all three plays of the Oresteia, the only extant tragic trilogy of ancient Athens. When she commits her kill, a jet of warm blood from her victim soaks her – as delightful and refreshing to her, she asserts, as the rain that Zeus sends to sustain the ripening ears of corn.

The first two plays of the trilogy, Agamemnon and The Libation Bearers, see a family locked into a nightmarish pattern of kill and counter-kill. The third, Eumenides, releases the drama from this blood-clotted atmosphere, this feedback loop of horror, and brings to bear civic, judicial processes that at last have the power to neutralise and contain the seemingly endless pattern of vengeance. Along the way, the scene has shifted from Argos to the Delphic oracle, and finally to the audience’s home city. Here, Eumenides presents an aetiology of Athens’ own newly reformed homicide court, the Areopagus (situated on a hill just north-west of the Acropolis, not far behind the right shoulders of the first audience). Its powers, hitherto wide-ranging and concentrated in the hands of the aristocracy, had been the focus of bloody democratic revolution in the decade preceding the premiere of the plays. The Oresteia, in short, with its grip on love, rage, murder, class, gender and the role of the state, is no drama for sissies.

The last major production in the UK was in 1999, when Katie Mitchell directed the plays at the National Theatre. This year, three significant productions – at Home in Manchester, and at the Almeida and the Globe theatres in London – are to be staged. In Manchester this autumn, the rising star Blanche McIntyre (who as a classics graduate is marinaded in Greek theatre) will direct “a radical, stripped back” production of Ted Hughes’s version, with the citizens of Manchester taking the role of the chorus – an intriguing prospect, given the civic questions the plays poses about how societies accommodate their most unruly and frightening elements. The Globe’s production, directed by Adele Thomas, will draw on a new translation by Rory Mullarkey. And at the Almeida, as part of that theatre’s Greek season, Robert Icke is directing his own “freehand” adaptation. The three taking on this great dramatic challenge in their different ways are young directors in their 20s or early 30s. For Icke, at least (whose production is the first to open, on 29 May), there is an urge to travel back to the very origins of European drama, and to investigate what these plays can tell us in 2015. How they can retain their freshness and excitement for an audience now? For Mullarkey, the plays pose a question of urgent import: “What does it mean when a society’s extreme elements are subsumed into the mainstream? Are these the compromises we all need to make in order to live together?”

The Oresteia, with its grip on love, rage, murder, class, gender and the role of the state, is no drama for sissies

Icke is intrigued by the plays’ significance as family dramas. Aeschylus sets Agamemnon and The Libation Bearers on the threshold of the royal palace. Here the king, Agamemnon, arrives home from his 10-year-long, victorious campaign in Troy. Here we see the despairing, vatic outpourings of his piece of human loot, the Trojan princess Cassandra, whose always accurate prophecies are never believed. Here, in one of the great scenes in theatre, Clytemnestra greets her husband as he’s on the point of entering the palace and outdoes him in verbal dexterity and persuasiveness, scoring a symbolic victory over him before she deals the actual death-blow. But the plays’ main events, the murders, take place behind closed doors, just out of sight of the audience. Icke, however, asserts the domestic setting and his adaptation will beckon us into this family’s interior world. In addition, the Oresteia’s “prequel” – Agamemnon’s sacrifice of his own daughter on the eve of his military expedition to Troy – is unhooked from the background of the drama and becomes a central event (in Aeschylus’s original, this story figures as a tale from the past narrated by a remembering chorus).

Icke also became fascinated by the formal daring of the dramas, especially the extraordinary scene at the end of The Libation Bearers. At this point, Orestes has just murdered his mother, Clytemnestra, who has murdered her husband, Agamemnon, who has killed their daughter Iphigenia (because the gods told him to, or, perhaps more accurately, because they apparently told him to). Just as the play ends, Orestes – a tortured, Hamlet-esque young man – is confronted by hideous apparitions, blood dripping from their eyes: these are the Furies, ancient spirits who seek vengeance for family murder. No one else can see them.

At the beginning of the third play, however, the Furies are embodied: they are, in fact, the play’s chorus, evident for all to see. For Icke, reading in the post-Freudian age, this opens up the possibility that the third play might occur entirely within Orestes’s disordered mind. It’s a fascinating notion, though one that may result in downplaying the change in atmosphere between the plays, a change that is partly contained in Aeschylus’s very language, and relates to the work’s wider politics. In Agamemnon in particular, the world of its words is jagged, bold and unbalanced – reflecting and creating the terrifying and confusing universe of the drama. Metaphors are unresolved and polysemic, a fact skilfully recognised by Icke when he has his characters debate the multiple possible meanings of the famous omen, in Agamemnon, of two eagles killing a pregnant hare.

Facebook Twitter Pinterest Robert Icke, directing at the Almeida. Photograph: Manuel Harlan

Considerably more clarity and light runs through the language of Eumenides, however. We have shifted away from the bizarre and frightening Argos, where, as the classicist Edith Hall points out, the queen quotes Egyptian poetry in her welcome-home speech and freakishly prostrates herself to her returning husband. (A practice that, for contemporary Greeks, was the sort of unacceptable act that belonged to the hated Persian court.) In Eumenides we are more recognisably “at home” – albeit a in mythical, long-ago version of Athens, where gods and the Furies wander freely among mortals and interfere directly in human lives.

More striking, though, than this supernatural element is the fact that Eumenides takes place in a city with no king – the only extant Greek tragedy to lack a royal ruler. This is a play about a kingless society, a democracy; it is about about presenting a mythical origin for modern institutions. It was the democrat Ephialtes who had reformed the aristocrat-dominated institution of the Areopagus, splitting up its decision-making powers between the popular assembly and other bodies but retaining its role as a homicide court. The Eumenides, in making Orestes the court’s first defendant, thus presented the Athenian audience with a story about the ancient origins of its (limited) powers. Ephialtes was assassinated in 461, three years before the play’s premiere in 458. It is, as Hall writes in a forthcoming essay, quite probable that his assassins were in that first audience. This play was extraordinarily close to the bone.

In the play’s trial, Athene, the goddess of the city (and of winning, and of cleverness) hears evidence. Apollo speaks for Orestes, and argues that his crime was no crime, because the mother is not truly a blood relative of the son: she is merely the container for the seed of the father – even by contemporary Athenian standards, a casuistical argument. Orestes cannot therefore be guilty of killing a family member. The jury votes, and is split evenly. Athene casts the deciding vote – and spares the mother-killer. As a goddess sprung from the head of her father, she asserts the superiority of the male.

“The Eumenides,” wrote Simone de Beauvoir in The Second Sex, “represents the triumph of the patriarchate over the matriarchate.” If one thing is clear in the Oresteia – and so much is not – it is the truth of De Beauvoir’s words, tucked away in a footnote of her masterpiece. The claims of the dead woman who spoke like a king, for whom action followed thought in the flick of a second, who called for a “man-slaying axe” in a moment of duress are all wiped out. And the Furies – those female, atavistic spirits – are suppressed and subsumed into the civic and religious life of the city; they are transformed and neutered into “kindly ones”, which is what “eumenides” means. Terror, from this moment forward, will be exerted not by frightening female spirits, but by the instruments of the state. So it is that the Oresteia dramatises democracy as it is invented – troublingly.

• The Oresteia is at the Almeida, London N1, from Friday to 18 July (almeida.co.uk); at the Globe, London SE1, from 19 August to 16 October (shakespearesglobe.com); and at Home, Manchester, from 23 October to 14 November (homemcr.org).