Is that a sabre you see before you? It could be if you’re talking any of multiple stage and screen versions of Hamlet, the Shakespeare play that puts centre-stage arguably the most esoteric of all Olympics activities: fencing. (Well, OK, beach volleyball is possibly just as rarefied, though it’s hard to imagine Hamlet and Laertes having much truck with that.)

We’re fresh out of superlatives. The Globe to Globe season has put a girdle around the earth in 37 languages, and the visiting companies have now left the building. You have to high-five the Globe’s chutzpah for mounting this wondrous contribution to London 2012’s World Shakespeare Festival in the first place. But in quite properly keeping the biggest till last, it surely took extra testicles to stage the famous play about a royal family in turmoil on this of all weekends.

First come the strip-lit corridors, the stained breeze blocks, the locked doors; later there are restraints, drugs, needles. The time is out of joint, and we are all imprisoned in a nightmare of confusion, paranoia, guilt and despair. Who are the mad? Who the sane? In Ian Rickson’s thrilling production of Shakespeare’s great tragedy, it’s often frighteningly unclear.

Lightning hasn't quite struck twice at the Theatre Royal Haymarket, where Trevor Nunn's dazzling reclamation of early Terence Rattigan (Flare Path) has been followed by the same director's transfer from Chichester of Rosencrantz and Guildenstern Are Dead, Tom Stoppard's first play. How does this 1966 gloss on Hamlet by way of Beckett hold up today? Engagingly enough, not least when its two tireless leads are in full existentialist flow. But some may nonetheless feel a degree of exhaustion, however much they'll want to cheer Samuel Barnett and Jamie Parker on.

Derek Jacobi (b 1938) grew up in Leytonstone. His father was a tobacconist, his mother worked in a department store. Although he entered the profession in the great age of social mobility in the early 1960s, no one could have predicted that he would go on to play so many English kings - Edward II, a couple of Henry VIIIs and Shakespeare’s two Richards - as well as a Spanish one in Don Carlos. This month he prepares to play another king of Albion: Lear, against which all classical actors past a certain age must finally measure themselves.

The relationship between stage and screen has always been fraught with antagonism and suspicion. One working in two dimensions, the other in three, they don't speak the same visual language. But recent events have helped to eat away at the status quo. On the one hand, theatre has grown increasingly intrigued by the design properties of film. Flat screens have popped up all over the place, notably in Katie Mitchell’s National shows and at the more ambitious work of the ENO. Meanwhile, theatre and opera have been encouraging those who, for reasons of distance or price, can’t make it to the show itself to catch it on a cinema screen instead.

The National Theatre’s new production of Hamlet is both a very good Hamlet, yet also a somehow disappointing one. For a work so rich in possibilities, with so much emotion, so much superb and intricate engineering, it is often like this, in England or anywhere else - inspiring and unconvincing at once.

It's an axiom trotted out in the acting profession that a young male actor measures himself against the role of Hamlet, much as an older one does with Lear. It's been announced this week that a couple more are having a stab at the Prince of Denmark. Michael Sheen will be the Young Vic's Dane in winter 2011, while Sheffield will see John Simm's this autumn. And we already know that the next tranche of Hamlets will also include Rory Kinnear at the National later this year

It is rare enough for directors to collaborate in theatre, even rarer in opera. Patrice Caurier (b. Paris, 1954) and Moshe Leiser (b. Antwerp, 1956) began their long collaboration in their 20s. They are now in their 50s, and since that first production of Britten’s A Midsummer Night’s Dream at Opéra de Lyon in 1982, they have never worked (or lived) apart. Cohabiting and collaborating, they are opera’s closest equivalent to Gilbert and George.

The BBC's reinvention of Doctor Who under the auspices of Russell T Davies has proved to be an inspired upgrade of a legendary 1960s marque fit to rank alongside BMW's resuscitation of the Mini, though it would hardly be sensible to argue that the new-look Doctor is distinguished by Germanic precision engineering or a coolly mathematical design philosophy. Quite the opposite.