Martin McDonagh's The Beauty Queen of Leenane, currently running at the Young Vic, is a feast of quotable lines and memorable scenes. But of all the reasons why this 1996 play consistently charms audiences and press alike – the black wit, the flashes of gore, the beautifully observed details of Irish life – surely the most powerful is the central figure of 70-year-old Mag Folan: a viciously manipulative mother locked into damaging co-dependency with her equally vicious 40-year-old virgin daughter.

When I saw Joe Hill-Gibbins's revival at the Young Vic last week, a particular frisson passed through the audience when Rosaleen Linehan, the 74-year-old actress playing Mag, took her bow. As we left the theatre, the comments around me all focused on either Mag or Rosaleen. "The whole Complan thing was a bit too close for comfort," said one middle-aged woman; "I remember trying to get the lumps out for my gran." "I wonder how old that actress is," said a man in his 20s, "she's so sharp." And I noticed several other young women shooting their mothers the same half-loving, half-terrified look I was directing at mine.

It was interesting that in a play full of sex, violence and madness, it was the simple fact of seeing age portrayed on stage that really shocked. Linehan's scrupulously detailed physical and emotional tics, from her sour, scrunched face and slurring speech to her resentful, habit-hardened mind, forced us to face up to one of our last societal taboos: ageing and how to handle it. Although we are horrified at the casually cruel way Derbhle Crotty's Maureen treats Mag, we are even more horrified at the thought that we might become trapped in lesser versions of her nightmarish scenario. With an ageing population showing the fastest growth in the "very old" (85+) category; the UK care homes scandal continuing to unfold; and increasingly nomadic, fragmented families displacing grandparents from their traditional protected niche, old people are becoming our next tranche of problematic refugees.

Theatre, largely unbound by Hollywood's obsession with youth, has always been a good place to play out the threats and opportunities posed by age. On film and TV, even the oldest actors are somehow softened and defused by the fourth wall of a screen; on stage, their energy, bodies and hearts are unmediated. In many parts of the world public drama had its roots in ancient funeral rites and oratories. We have long used the proximity of death as a tool to probe the meaning of life.

One of the most memorable figures of Greek tragedy is the old king Oedipus, blinded, ostracised and led from Thebes by his adoring, despairing daughter. He is a precursor to Shakespeare's King Lear, and although Lear describes himself as a "poor, infirm, weak, and despised old man" it is in fact the enduring force of these men that frightens the generation below. Oedipus becomes a walking symbol of the murderous, incestuous darkness at the heart of Greek royalty, while Lear's fury and fearlessness in the storm reminds audiences that, freed from the petty political squabbles of court, in many ways the old have nothing to lose. To move forward, both societies must find ways to reconcile themselves to these ageing men. Only by embracing and learning from history can they create a future.

I will never forget Michael Gambon's 2004 turn as Hamm in Samuel Beckett's aptly named Endgame. In this play, it is not just the man in the wheelchair before us who is threadbare and dispossessed; the world is ageing too. Gambon played Hamm as a monster of redundancy: a great, flailing embroidered lump grasping for the vestiges of his power with petty, pathetic cruelty; but he was also cuttingly wise and eloquent and funny, and certainly no more pathetic than Lee Evans's inept young Clov. Gambon's inimitable voice, at once vulnerable and brutal, lyrical and booming, captured the dichotomy at the centre of the play: the interdependent glory and grotesquery of man, not diminished but distilled by the passing of the years.

Of course, age has always provided fertile territory for comedy, too: the Lady Bracknells and the Falstaffs sneer and stumble their way through our collective consciousness with bittersweet joy. We put age on stage to celebrate, not just to examine it, and it can exhilarate us as much as it makes us uncomfortable. But, returning to Linehan, I suspect that the aspect of her performance that thrilled us the most was to see age playing age.

Watching older actors so brilliantly nail a part – and watching them literally play with the one trait of which all of us are supposed to be embarrassed or ashamed, which they are supposed to mask with vigorous work-outs and anti-wrinkle face creams – leaves us unable to despair or patronise. Age is no different to anything else; it can bring wisdom or idiocy, energy or incapacity, just as youth can mean beauty or folly. But whatever form it takes, it always brings with it an added layer of mystery and complexity that makes for theatrical gold. What actor, after all, would choose Romeo over Lear?