The National Theatre tonight hosts its 50th-birthday gala, 11 days after the English-speaking theatre's most important and influential address in fact reached the half-century mark. With celebration comes recollection, not least for those of us for whom the brutalist portals of Denys Lasdun's concrete structure have come over the years to seem nothing less than a second home. 

How irksome in some ways for the National Theatre that both the glamour and the accessibility of cinema have bookended its first 50 years, when the company and, latterly, its Southbank home, are essentially driven by and dedicated to live performance. But it was Laurence Olivier’s film career, making him a household name, which helped secure for him the job as first director of the National Theatre in 1963. And it is cinema relays that have taken NT productions to places and people who might never step into Denys Lasdun’s building, despite the company’s national ambitions.

The sixth artistic director of the National Theatre of Great Britain will be Rufus Norris, it was announced this morning. Bookies’ favourites such as Marianne Elliott, Michael Grandage and Dominic Cooke having long since ruled themselves out, Norris can be welcomed as a daring choice. For a start, unlike most of predecessors apart from Hytner, he has never run a large theatre company – although he has been an associate down the road at the Young Vic and at the National itself.

Once upon a time, there were two cultures, and they were at odds. A forested wilderness stretches between the kingdoms of Sealand and Lagobel, as we glean from the childishly-drawn, giant map that serves as a front cloth for the NT's new musical spectacular – directed by Marianne Elliot and opening in the Lyttelton last night. The map shows, on one side of the wilderness, Sealand’s coastal realm with winding rivers and a chateau bristling with turrets, all in shades of blue.

Shallow in its cartoonish whizz through the tergiversations of a troubled reign, hugely energetic in its language and structured storytelling, Marlowe’s horrible history is never less than compelling and challenging at the National. It may have found its best match yet in the collapsible bric-à-brac pageantry of Joe Hill-Gibbins’ vivid, in-your-face production.

Sicilian location, Irish populace, Balkan Roma music: Richard Eyre’s production of a Pirandello bagatelle could easily have turned into the kind of Europudding more common in cinema. That it fairly dances over the pitfalls is due partly to a well-calibrated ensemble, but above all to the fact that the great Italian playwright made an exception to social commentary and searching examination of the human condition, coming up instead with a piece of fluff about babymaking village-style.

Oh, how the mighty are fallen. Margaret Alexander (Marianne Jean-Baptiste) is a storefront pastor in Harlem who leads her flock with absolutist conviction. No drinking, no smoking - the way to the Lord is through abstinence and clean living, and she herself embodies these righteous goals. So woe betide Sister Margaret when her far from clean-living ex-husband, a musician called Luke (Lucian Msamati), arrives at her door after many years.

One of the promises of artistic director Nicholas Hytner when he took the helm of this flagship 10 years ago was to stage new and innovative musicals. His problem, of course, is that these don’t grow on trees. So after the triumph of Jerry Springer: The Opera in 2003, we had to wait eight years for London Road, the venue’s next British hit. In the meantime, the United States has occasionally plugged the gap — and now provides this current musical, in the shape of a critique of American capitalism by New York’s the TEAM.

“My three men,” declares the deeply compromised heroine of this 1928 experimental drama by Eugene O’Neill. “I am whole.” Nina Leeds – hungry for love, ruthless with her own heart and those of others – burns like the sun at the play’s centre. She is given a portrayal by Anne-Marie Duff, in this fine production by Simon Godwin, so scorching that she all but self-immolates, while her men circle her like planets, helpless to alter their course. It is an impressive achievement – even if the work itself remains unwieldy and unsatisfying.

The Oliviers consider more than twice the number of productions for their annual awards compared to Broadway's Tonys. But you could be forgiven for thinking otherwise following Sunday night's 37th annual shindig, which divvied up the kudos among notably few recipients, The Curious Incident of the Dog in the Night-Time leading the pack with seven awards - on a par with Matilda this time last year. At the same time, many other worthy hopefuls went home empty-handed, if they were lucky enough to get nominated to begin with.