The National Theatre's new Dorfman auditorium gets off to a kick-ass start with Here Lies Love, the Off Broadway musical transplant that does for the closing months of Nicholas Hytner's tenure as artistic director what Jerry Springer the Opera did for the early days of his regime a decade or more ago.

Purists may take issue with Anya Reiss’s incursion into the classics. Having already tackled The Seagull and Three Sisters, she’s now turned her dogged 21^st-century gaze on Uncle Vanya. But Reiss’s adaptation, though fresh and punchy, is notable, in fact, for its amiable fidelity. The framing is in place for a provocative revamp, yet, in appropriately Chekhovian fashion, Reiss appears to have hit some kind of a psychological barrier partway through the process.

When unveiling her first season at Sherman Cymru earlier this year, new artistic director Rachel O’Riordan gave voice to two ambitions: to generate new writing within Wales, and produce classic texts which specifically resonate with the audience. What better way to begin than with Shakespeare’s famous tale of star-crossed lovers?

Like Ibsen’s titanic character in search of a self, the Barbican’s theatre programme globetrots to find the richest and rarest. Yet it certainly doesn’t reach Peer Gynt's conclusion that home's best. In this case London’s finest and, for most of the year, only showcase for the most innovative of world theatre looked as if it might be hoist with its own international petard: I doubt I’ll ever see a production of Ibsen’s epic masterpiece as shatteringly great as Baltasur Kormakur's pared-down vision for the National Theatre of Iceland in the Pit back in 2007.

Are there any real taboos left? I mean, there have been scores of plays about incest, about abuse and about paedophilia. Have all proverbial stones been turned over? According to Deborah Bruce, a director turned playwright, there is one situation that still troubles people, especially women: it is mothers who leave their children. Although this is a staple of women’s magazines, there have been few plays about the subject. So Bruce’s new drama is welcome — and it comes with the always watchable Helen Baxendale as its star.

It’s hard to believe that almost two years have passed since Phyllida Lloyd’s Julius Caesar at the Donmar Warehouse. Harriet Walter’s stricken face as the play ended is still burningly fresh in the memory as we return to the theatre for Henry IV – Part II of a planned trilogy of all-female Shakespeare plays. Incarcerating us once again in a women’s prison, can the power of Lloyd’s conceit survive a second outing?

“I am spiteful! I am ill! You are not going to like this!” With these words Harry Lloyd opens his one-man show that adapts the Dostoevsky 1864 novella that is often hailed as the first work of literary existentialism. Lloyd is already on stage as the audience enter, darkly bearded, sitting in a dishevelled armchair on a floor created from stacked books beneath his bare feet, his haunted piercing eyes following viewers as they take their seats.

It's tempting with this show less to write a review per se than to simply pile on the puns, but that would be to piss on - sorry, I meant do a disservice to - both the musical that is Urinetown and to the exceptionally deft UK premiere that the Broadway sleeper hit from a dozen or more years ago is currently receiving at the hands of the director Jamie Lloyd. In New York, Tony-winners Mark Hollmann and Greg Kotis's wilfully self-conscious pastiche was by turns winning and wearing, in accordance with a piece that has barely begun before it starts to self-deconstruct.

The advantage of basing drama on real events, particularly emotive ones like the 2005 London bombings, is that they have inbuilt resonance; the disadvantage, all too apparent in 2013 play Warde Street, is that it can be challenging to articulate a revelatory view. Familiarity with the arguments and sentiments expressed in this 80-minute piece vastly lessens its impact, and a burst of late tension (chiefly earned via the shortcut of a firearm) is further diminished by dubious use of reverse chronology. It’s a short play with grand ambition, sadly unfulfilled.

To do Mamet’s work justice, you must be able to deliver dialogue with the speed, skill and breathtaking bravura confidence of Usain Bolt. In Lindsay Posner’s much-hyped but frustratingly sluggish revival at the Playhouse Theatre, only one of three cast members rises to that challenge – and it’s the one who’s generated by far the fewest column inches. British actor Nigel Lindsay is the breakout star of a strange experiment in meta-satire, in which Mamet’s denunciation of a movie-going public allowing crass commercialism to override creative integrity gains surreal significance.