Men are bastards. Okay, not all of us, but enough to make the lives of millions of women a misery. This we know, but anyone who has any doubts might be educated by some of the horrific statistics of sexual assault and domestic violence in the programme of Deborah Bruce’s Dixon and Daughters, a new play at the Dorfman space of the National Theatre.

It's saying a lot when a production lives up to its gasp-inducing set. That's the happy case with Josie Rourke's loving revival of Dancing at Lughnasa, which returns Brian Friel's modern-day classic to the building, the National, where this Olivier and Tony Award-winner first played London over 32 years ago.

Buildings can hold memories, the three dimensions of space supplemented by the fourth of time. Ten years ago, I started every working week with a meeting in a room that, for decades, had been used to conduct autopsies – I felt a little chill occasionally, as we dissected figures rather than bodies, ghosts lingering, as they do. 

How can old texts speak to us now? The point is not just to adapt classics, but to reimagine them – and that’s exactly what hotshot Australian director Simon Stone does. Having brilliantly staged Lorca’s Yerma with Billie Piper, he now turns his attention to Phaedra, creating an amazing and thrilling mash up of the myth as told by Euripides, Seneca and Racine.

Is British new writing in deep trouble? With the Arts Council defunding venues such as the Hampstead Theatre, the Donmar and the Gate, and past masters such as Terry Johnson underperforming, the signs are not good. But what about the National Theatre, the country’s flagship — can it step up to fill the gap? Well, judging by recent flops such as Moira Buffini’s Manor, I wouldn’t bank on it.

Clint Dyer is the first black director of Othello at the National Theatre, a venue that once staged the piece with its actor founder Laurence Olivier playing the lead role in blackface. 

Hovering way, way above us, three aptly named high fairies, in voluminous chiffon, open a show that may not be airy in the metaphorical sense, but invites us to cast our eyes upwards continually – no bad thing to do in the bleak midwinter of 2022. But does the show, delayed after one Covid cancellation after another on its spluttering debut 12 months ago, soar as a new show should? Give or take the odd clunky landing, it does.

The cynical might think Pearl Cleage’s play had been expressly written to address the over-riding issues in today’s USA – abortion and contraception rights, gun control, homophobia, racism. But the cynical would be wrong, as Blues for an Alabama Sky was written in 1995. What is notable is its timely scheduling by the National Theatre.

It’s particularly poignant to watch this story in the knowledge that a little over a year after US-led troops withdrew from Afghanistan, women and girls are enduring a renewed repression of their rights under the Taliban. The real-life story of The Boy with Two Hearts took place in 2000 – the year before the western invasion began; to see it today is a depressing reminder of how little was achieved through that ill-thought-out venture.

How can this beauty arise from such ugliness? The Crucible, Arthur Miller’s 1953 drama about the Salem witch trials of 1692, is rife with unwavering prejudices, selfish slander, and sickening motives. But under Lyndsey Turner’s aesthetically vigorous direction on the National Theatre’s Olivier stage, the play’s infected air becomes a breeding ground for visually arresting tableaux possessed of rampant emotional intensity.