David Baddiel last did solo stand-up in 2004, when he walked out of a corporate gig after calling a bunch of bankers the c-word. Since then, he's spent his time mostly writing novels and doing some television and radio projects. It's his general absence from TV, he tells us in Fame: Not the Musical - an intelligent, witty and thoughtful examination of modern celebrity - that arouses pity in some members of the public who recognise him. If he's not on the telly, his career must be on the skids, right?

Science has fallen in love with comedy – or maybe that should be the other way round. Whichever, geek is now chic, and being in possession of a brain is something to be laughed with, rather than at. All of which explains the popularity of Radio 4's The Infinite Monkey Cage, or Dara Ó Briain's School of Hard Sums on the Dave channel, both of which employ a large dose of comedy to discuss some terrifically complex topics.

If such a thing were to exist, then American essayist, humorist and raconteur David Sedaris would be a Radio 4 superstar. His broadcasts on the channel receive hit numbers and are repeated regularly, and he's a permanent fixture on those parts of the literary festival circuit that its listeners flock to. He's now touring the UK and it's sure to sell out, but it was interesting to see that his audience at Cadogan Hall was far more diverse than the channel's supposed typical listener – white, middle-class and 56 - might suggest.

My, what an entrance Jack Whitehall makes on the last night of his first arena tour. The 25-year-old - not that long ago making his Edinburgh Fringe debut - rides into the arena on a Segway with music blaring and fireworks. But he may have overreached himself, however, as a whole tier was curtained off and the remaining two were by no means full.

What a career arc Miranda Hart has had; from playing tiny venues at the Edinburgh Fringe in the early 2000s, followed by roles in television comedies including Hyperdrive, Lead Balloon and Not Going Out, to starring in her own sitcom, Miranda, and in the BBC One drama Call the Midwife. And now she is returning to live comedy not with a few dates in standard-size venues, but with an extensive arena tour.

It's a mark of Miles Jupp's charm that he can do a show with a long segment about being the father of four young children and win over both non-parents and those who wish to forget for two hours that they have left their own offspring at home with a babysitter. But in Miles Jupp Is the Chap You're Thinking Of, which I saw at the Ambassadors Theatre in London, the comic expounds at length on life chez Jupp, which appears to be a whirl of cleaning Weetabix-encrusted crockery and finding faecal matter in inappropriate places.

Young Irish actress and comic Aisling Bea made a tremendous debut with C'est la Bea at last year's Edinburgh Fringe, where she was deservedly nominated for best newcomer in the Foster's Edinburgh Comedy Awards. Now she is performing a short run at the Soho Theatre and, on second view, it's still a joyously funny show.

In Irish mythology, a stray sod is an enchanted piece of grass that, if stepped on, leaves a person feeling disorientated and lost, even in familiar surroundings. Although there's no reference to this in Tommy Tiernan's new show, Stray Sod, there's plenty of self-knowing stage Irishness – even, briefly, Oirishness – as he delivers a riveting 80 minutes of comedy that's a sort of state-of-the-nation address about his home country.

John Kearns introduces himself as himself as he comes on stage then, very carefully - tenderly almost - he lays out a blonde wig, a pair of women's high-heeled shoes and a skimpy dress on the floor. They stay there until the final segment of his show, untouched and without mention. He puts on a ridiculous oversize tonsure wig and a pair of joke-shop false teeth. Oh and he is wearing a horse costume, and “rides” Trigger as he performs the first bit of the show - which he tells us is about "disguise, expectations and failures".

Jane Bussmann may not be an immediately familiar name to some, but you will know her work. The writer, who was once a celebrity journalist, has been part of the writing teams for South Park, Smack the Pony and Brass Eye, among other quality television comedies, and wrote a hilarious memoir, The Worst Date Ever, about how a reckless whim took her to war-torn Uganda, where she helped unveil the appalling crimes of rebel leader Joseph Kony.