In 1913 a 25-old-year mathematician from Tamil Nadu sailed to England. He journeyed at the behest of a Cambridge professor who had been mesmerised by the display of untutored genius evident in the young Indian’s correspondence. Within four years the visitor had grown so depressed by his isolation that he attempted to throw himself under a train.

The longest and most densely historical play by Georg Büchner (1813-37) is a potential monster. In German, Dantons Tod can run to four hours or more. There's little action and much speechifying. In plays by his equally wordy, history-obsessed predecessor, Friedrich von Schiller, there are at least fights, battles, a lot of love - and some sex.

Political playwright Howard Brenton (b. 1942) is always in the process of being "rediscovered". Yet at the same time he has been at the heart of British theatrical life for the past 40 years, since his debut in 1969 with Christie in Love. True, he has spent the odd decade out of the theatrical limelight - a few years ago, he "went out of fashion" in his own phrase – and then he just happened to pen some of the liveliest scripts on television with the BBC’s spy drama series, Spooks (2002-2005).

“Tragedy reminds us how to live,” declares Moira Buffini’s democratically elected heroine, Eurydice. It’s a reminder the playwright herself and her latest work, Welcome to Thebes, is eager to provide. Following on the well-worn heels of last season’s Mother Courage at the National comes a new play that once again places women in the front line. Leaving to Brecht the barren fields of Western Europe, Buffini sets up her stall in the fertile dramatic ground of contemporary Africa – a place where gang-rape and murder are just the prologue.

A pall of ennui hangs over the 1930s drawing room of the National’s latest Rattigan revival, as deadly as the boredom its burnt-out party people all dread. The trouble is, I’m not sure to what extent the playwright intended it.To write about the etiolated and the unfocused, the lost souls of the inter-war years, needs energy and clarity.

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

The recent fuss about British culture being anti-Catholic just because some civil servant wrote a spoof memo satirising the Pope’s upcoming visit may have been overblown, but it is certainly true that, in the past, Italy was a byword for rank corruption. To doughty English Protestants, Rome was a stew of sin and Italians were Machiavellian plotters and idolators. Little wonder that Thomas Middleton’s 1621 tragedy, a large-stage revival of which opened yesterday, is brimful of illicit sex, cunning intrigues and vicious revenge - and set in Renaissance Italy.

No stars, minimal hype, a long afternoon into the South Bank night: the National Theatre is staging back to back two little-known plays by two 20th-century American masters, and the result is a bit like opening an old trunk in the attic to find pristinely laundered shirts and suits, and perhaps a pair of perfect spats. Beyond the Horizon by Eugene O'Neill and Spring Storm by Tennessee Williams are early works by each playwright, from 1920 and 1937 respectively, and while the O'Neill feels somewhat stretched, even lugubrious, it's astonishing to learn that Williams' ebullient piece was first performed only in 1996.

It takes a particular talent to poke fun at the Russian Revolution and its aftermath, a conflict that cost millions of lives and led to one of the most brutal regimes in modern history. But Mikhail Bulgakov’s novel, which he later turned into a play and is presented at the Lyttelton Theatre in a new version by Andrew Upton, does just that. It’s a big, rambling, sometimes confusing affair that dips into farce, but one that remains entirely gripping throughout its two hours and 40 minutes.