To the list of abiding theatrical partnerships one must surely add Tom Stoppard and the director David Leveaux. From his Tony-winning revival of The Real Thing onwards to Jumpers and Arcadia, all of which played both London and Broadway, Leveaux has proved a particularly dab hand at mining this playwright in all his near-infinite variety.

I avoided seeing Art when it was first staged in 1996, even though Matthew Warchus’ production created a huge buzz and won an Olivier Award for Comedy. (On receiving the award, Yasmina Reza joked that she thought she’d written a tragedy not a comedy.)

The signs were there early in Glenda Jackson's career that she would one day have what it takes to "ascend the Everest" (as the cliché has it) of Lear. So powerful was her performance as Ophelia in Peter Hall's production of Hamlet in 1965 that there was talk afterwards of her being cast as the prince himself. Two years later she was another disturbed woman playing Charlotte Corday unforgettably whipping Marat with her hair in The Marat/Sade.

Nobody said that a 70-minute audience with the undead was going to be easy. You can read Samuel Beckett's Texts for Nothing in your own time, pausing for thought, leaving off, coming back. When as compelling an actor as Lisa Dwan chooses not just to read it but to perform a selection for the first time, there's nowhere to hide – either for us or for her.

From time to time theatre managements hit on the idea that danced drama should be part of their remit. Nick Hytner flirted with it at the National in his day with a run of productions for Lloyd Newson and his company DV8. Now Matthew Warchus, his feet barely under the desk at the Old Vic, has commissioned a show from a young choreographer who has Matthew Bourne’s crown in his sights.

It’s raining. Well, of course – it’s April in London. But it’s also pouring down on the Old Vic stage, hammering an already battered slate roof. When it lifts to reveal the semi-derelict attic, site of Harold Pinter’s groundbreaking 1960 play, the rain stays in your mind: an outside world that can be merciless towards the weak. And in Matthew Warchus’s revival, the trapped trio are very much victims – of one another, of society, and of their own failings.

Demons, trolls and dead souls have a habit of latching onto Ibsen's bourgeois Norwegians. Surely the best way for actors to handle them is to keep it natural, make them part of the furniture and, in Dostoyevsky's words, "render the supernatural so real that one is almost forced to believe it". But very little seems real or spontaneous in Matthew Warchus's production of The Master Builder.

You'll feel guilty for having bothered with a programme after seeing The Lorax, the Dr Seuss adaptation that puts saving the environment centre-stage at the Old Vic just as the recent climate change gathering in Paris has done on the world stage. Full of unimpeachably good intentions, the production is fun and frolicsome up to a point, and sometimes simply bewildering.

Never use one word when you can get away with two: that seems to have been the maxim of Eugene O’Neill even in one of his shorter plays. After all, when is an ape not hairy, and why does stoker Robert “Yank” Smith, a natural hulk brought low by mechanised capital, have to bang home the title at every opportunity? Yes, this must have been an astonishing play to see on Broadway in 1922, and it still gives director Richard Jones a chance to throw every stylised trick in his very singular book at its eight diverse scenes. But masterpiece it isn’t.

Can we – should we – control the future? That’s the dilemma faced by anxious parents attempting to steer their offspring through a labyrinthine school system, educational think-tanks, and the teachers shaping young lives. Tamsin Oglesby’s play is an intriguing opener for the Matthew Warchus era: impassioned, fiercely topical, and – with its relatively youthful cast – kicking against the “old” in “Old Vic”. That, and electric guitars as rousing musical accompaniment. The school of rock is now in session.