As its first gift to dance fans, the new year has delivered not one but two chamber pieces about extraordinary women. Down in Covent Garden this week, Will Tuckett's Elizabeth for Royal Ballet dancers is exploring the life and loves of Queen Elizabeth I, while up in Camden Akram Khan's Until the Lions takes a fresh look at the story of princess Amba, from the Indian classical epic the Mahabharata.

So, Andrew Davies has bitten off the big one. It may have come as a surprise to some that the master of adapting the British classics for television hadn’t read Tolstoy’s classic-to-end-all-classics until the BBC mooted the idea of a new screen version, but this first episode (of six) boded very well all the same.

If Matthew Bourne never made another story ballet, his company New Adventures could probably carry on touring his back catalogue till the end of time. The Sleeping Beauty is only on its second London outing, and although it lacks the emotional clout of his Swan Lake, it’s clearly set for a similarly long life as a Great British Export.

Is Jim Broadbent Britain’s best-loved actor? The slate of screen roles he’s accumulated over the years – this Christmas Carol is his return to theatre after a decade away – has surely given him a very special quality in the nation's consciousness, a combination of general benignity with more than a hint of absent-mindedness, an almost madcap bafflement at the world.

One of the joys about this stage adaptation of Jules Verne’s Around the World in 80 Days is the contrast between its phlegmatic hero Phileas Fogg, who deals with everything in terms of precision and logic, and the picaresque confusion of his journey. Fogg (Robert Portal) has the habit of laying down portentous truths in an attempt to mediate the scampering mix-ups that he encounters at every stage. One such aperçu, “A well-used minimum suffices for anything,” serves nicely as a verdict on Lucy Bailey’s energetic, engaging production.

I adapted Around the World in Eighty Days very specifically for my own theatre company, Lookingglass Theatre of Chicago, where I am one of 24 multi-skilled ensemble members who are writers, directors, actors, and/or designers. Although Lookingglass’ work varies, we most often do adaptations of classic stories, frequently epic in scale, told in a highly theatrical, strongly visual and/or physical way.

If the title wasn’t already occupied, television-wise, the BBC might have titled Capital “The Street”. It’s got the high soar-aways over urban geography that recall the soaps, but here they spread wider, taking in a metropolis. It’s “capital” as in London, and we may wonder just who’s been padding around the premises before John Lanchester’s 2012 novel, from which Peter Bowker’s three-part drama is adapted.

The real achievement of this remarkable DVD release from the BFI is the fact that it brings the name of George Hoellering back to our attention as a director. His 1951 adaption of TS Eliot’s verse play Murder in the Cathedral has been virtually unavailable for years, and is the centrepiece of his career, while the accompanying documentaries here reveal a fascinating and diverse talent.

Patrick Barlow’s last play was parked in the West End for nine years. The 39 Steps finally closed this autumn, but not before travelling all over the world, most prestigiously to Broadway but also, among other destinations, to Russia, Japan, Australia, Korea, Hong Kong and France. There have been no fewer than eight different productions in Germany, including one with an all-female cast. So the question naturally pinging around Barlow’s cranium was: how exactly do you follow that?

Saoirse Ronan, emerging decorously into womanliness in Brooklyn, deserves a stack of awards nominations for her portrayal of a brave young woman torn between her old life in Ireland and her new existence in 1952 New York's most vibrant borough. Restraining her character’s flickers of doubt, culpability, satisfaction, and pleasure, Ronan shows how the maturation of Eilis Lacey – from seasick voyager and homesick immigrant to serene resident – is attributable to her hard-won stoicism and quiet determination.