Dave Gorman was probably the first comic to have embraced technology in his stand-up. Albeit, in the early days, it was using 35mm slides, hand-drawn graphs and an overhead projector, but then latterly a computer and the ever-more influential Internet and social media. And so, as is a feature at all his shows, there's a large screen on stage when I see him at the Royal Festival Hall and when he says: “I've put it on a graph” there's a loud cheer of recognition from the audience.

Eddie Izzard tells us at the top of a show lasting two-and-a-half hours that he's on the home straight in a mammoth tour taking in 28 countries. He first performed Force Majeure in 2013 and now, in a slightly rebooted form, he parks it in the West End for an extended run as Force Majeure Reloaded.

When Anne Edmonds comes on stage I notice a banjo sitting ominously in a corner. She is full of Australian bonhomie and energy, instantly connecting with the audience, and our first impression is that she's a likeable chatterbox, telling anecdotes without punchlines - and she begins with a lengthy one about spewing copiously on a New Year's Day flight in front of her parents some years ago.

What a trouper Bill Bailey is. Just as he's introducing what is clearly meant to be a showstopper in which he and the audience would create a number in the style of “maestro of melancholia” Moby, his technology lets him down. But no fear, Bailey ad libs for several minutes as he tries to rectify the problem, knocks out an Irish reel on one of the many instruments on stage, and moves on when it's clear that the “Moby song" will have to remain unsung.

The show's title, Outside, Looking In, might suggest we're in for some philosophising from Ed Byrne – but then, after 22 years in the business, the Irish observational comic has earned the right. And indeed, he covers subjects such as feminism, slut-shaming and gender imbalance, but in the mix there is also some material about the perils of dating and a graphic description of food poisoning. Even the cleverest comics – and Byrne is assuredly one of those – can't resist the occasional lavatorial gag.

Loadsamoney stomps on clutching a wad of twenties. He hasn’t been seen since the Eighties, he advises, because he became irrelevant. In the strict sense Harry Enfield and Paul Whitehouse have never been relevant. Relevant comedy has a habit of becoming irrelevant, which is why their Legends! tour is such a treat for audiences over a certain age. It issues a gloriously defiant two-fingered salute to time and tide and political correctness (we are welcomed as “ladies and gentlemen and transsexuals”).

When is a comedian not funny? Dawn French has spent so much of her life making audiences laugh that her debut as a one-woman performer requires some recalibration. The next-door smile is as big as ever, and the eagerness to be liked, so the early section – about the thieving march of time – looks and sounds like a stand-up routine that isn’t quite landing. Laughs are thin on the ground. It’s only about 20 minutes in, as she tells of her early childhood on an Air Force base in Yorkshire, that her intentions begin swimming into proper focus.

It may seem strange to begin a review of a comedy gig with a description of the Tube journey home. But it was noticeable that the crowds who left the O2 Arena in London after Michael McIntyre's new show Happy & Glorious weren't talking about it. About the weather, the full train, what they were up to at the weekend, yes; but his show, no.

Alan Carr has titled his latest live show Yap, Yap, Yap! Because, he says as the show opens, everyone has too much to say these days, much of it - such as the stuff on Twitter - not worth listening to. Coming from the host of Channel 4 chatshow Chatty Man, that's comically rich. But such is Carr's genuine likeability that the audience overlook that and settle in to enjoy the evening.

Sam Simmons' new show – for which he won the Edinburgh Comedy Award last month and the Barry award at Melbourne earlier this year – is titled Spaghetti for Breakfast, but could easily be called “Things That Shit Me”; the phrase pops up repeatedly on a recorded loop, as the Australian comic runs through the large number of things that annoy him.

The hour-long show is the surrealist comedian's most personal yet; among the wonderfully silly clowning, the comic delivers painfully honest anecdotes about his childhood, which help explain “why I turned out this weird”.