Massachusetts-born Bo Burnham first performed in the UK at the 2010 Edinburgh Fringe. The then teenage prodigy, who had come to fame as a YouTube sensation, took the festival by storm and was given the Edinburgh Comedy Awards' panel prize. He hasn't performed here again until this year's Fringe, when his second stage show, What, sold out in a matter of minutes and was again garlanded with rave reviews.

Sarah Millican’s career blossomed on the back of a divorce. Her husband upped sticks after seven years of marriage when she was 29. The rage and sorrow catapulted an innately funny office worker into a second career. For her new show, entitled Home Bird, the story has moved on and her subject is buying a home and installing her boyfriend. Only he’s not happy with the arrangements in the garden. The shed, he complains, is not suitable for self-abuse. That, Millican explains, is because it’s a greenhouse.

Most years at the Fringe, there's considerable division over the winner of the Edinburgh Comedy Award, but not in 2013 when Bridget Christie won for A Bic For Her, a show that expertly fillets everyday sexism and misogyny. Even those who remarked that they never knew feminism could be funny - idiots all, of course - acknowledged the show is an hour of superbly crafted comedy.

When Andrew Maxwell premiered Banana Kingdom at the Edinburgh Fringe earlier this year, its title made a lot more sense. The show was a coruscating examination of what Scotland might be if the independence vote next September goes Alex Salmond's way; a tiny nation trying to go it alone at a time when the rest of Europe wants to be an even bigger - and of course happier - family.

Mancunian Jason Manford is the kind of chap it would be difficult to dislike. Laidback, casually dressed, smiley and interacting with his audience in a totally unthreatening manner - it's no wonder that that demeanour, coupled with his everyman observational comedy, has made him a star.

He comes on stage to tell us there's no support act. “I'm not paying someone 60 quid to be slightly shitter than me,” he says. And then he deadpans: “I can do that.” He's joking, of course, as he's not shit at all, but rather an accomplished entertainer.

At one point during the show Bill Bailey makes an aside about the last words of biologist JBS Haldane which were, according to the comedian, a comment about God having an “inordinate fondness for beetles". He then goes into a routine about deathbed quotations and the likelihood of coming out with a corker then having a snooze and muttering a mundanity just before you croak.

We're advised to take off our shoes, as the show will knock our socks off; it's the first of many neatly worked bits of wordplay about how good the show will be - “Is there anybody named Annette in the audience? Good, because this is comedy without Annette” - in a fantastic opening riff before Shenoah Allen and Mark Chavez get down to the proper business of the evening. Entitled Just the Two of Each of Us, this is another of their trademark shows of madcap physical storytelling, in which they each play several characters, with the only props on stage being two chairs.

The front rows of an Abandonman gig are not a place for shy people. The core of rapping Irish comedian Rob Broderick’s act has long been to interact with the audience and turn the nuggets he gleans into ridiculous songs. For his latest show, Moonrock Boombox, which he now brings to the Brighton Comedy Festival, he turns the crowd participation into a surreal space adventure. It’s fortunate, then, since we’re sitting in row three, that my girlfriend is not especially shy for she became a key player in Abandonman’s mission across the cosmos.

Russell Brand, as I've written before, divides the room. Well, not the beautifully refurbished 3,000-seat Hammersmith Odeon in London, where his faithful gathered for the past two nights on his mammoth international tour, but more generally. There are those who find his – and I use the word deliberately – cocksureness irritating, or his loquacity a ridiculous affectation.

Internet porn, the sexualisation of childhood and the objectification of women are so commonplace in Western society that they go mostly unmentioned and unchallenged, even in the arts. So thank goodness for performance artist and comic Bryony Kimmings, who not only mentions and challenges these pernicious forces in so-called civilised society, but in Credible Likeable Superstar Role Model, an award-winning show first seen at Edinburgh Fringe, fashions an entertaining show around them.