It will come as no surprise that a critic should instantly become a fan of a comic whose debut show at the Edinburgh Fringe (for which Alun Cochrane received a Perrier Award nomination) was a show titled My Favourite Words in My Best Stories. Anyone who loves words is a hit with me - we’re ploughing the same furrow after all, just in different ways.

It takes a very talented comic indeed to warm the main room at the Leicester Square Theatre, a venue that is situated beneath a Catholic church and which, vampire-like, can suck the life out of even the most buoyant of audiences. Fortunately, Jason Byrne has enough energy to wake the dead or, in this case, a few hundred damp souls who have come in from a rainy London town outside.

Nowadays, stand-ups who can fill the Enormodome grow on trees. But once upon a time, before comedy was the new rock’n’roll, that sort of thing didn’t happen. Then David Baddiel and Rob Newman played Wembley Arena. It feels like a long time ago. While Newman’s career wandered off the map, Baddiel became exceptionally celebrated as, in effect, Frank Skinner’s straight man. He last did stand-up in 2003, and that was a corporate gig to a roomful of bankers he deliberately offended. Last night he stepped back before an audience to – as he more than once insisted - try out some stuff.

Felicity Fitz-Frisky and Hansel Amadeus Mannish (aka Laura Corcoran and Matthew Jones) describe their act as “twisted pop cabaret” but that doesn’t begin to encapsulate a show that expertly parodies modern music. An easy target, you think, but this duo bring real singing and musical talent, plus a deliciously bitchy touch to the subject.

I have a friend who loves telling jokes. One night he started a well-worn story: “Please,” he said, “if you’ve heard this before, don’t stop me – it’s one of my favourites.” I am always reminded of that evening when watching Les Ballets Trockadero de Monte Carlo – the Trocks to their many thousands of fans across the world – when they touch down in London on one of their regular stops. The jokes are great – the dance is pretty good too – and if the jokes are a bit familiar, well, that’s all part of the fun.

Mindful that Dara Ó Briain ticked off one of my colleagues for revealing a punchline of his in his show, I can lumber without fear into reporting Rich Hall’s outing at the Wilde Theatre, Bracknell, as punchlines aren’t really what his comedy is all about. Morose as he looks on TV, on this very early date in an exhaustive 63-gig tour over the British Isles between now and December - I mean, Cambridge, Taunton, Dublin on consecutive days, or Hartlepool, Dundee, Durham (what is he travelling in? A helicopter?) - Hall had the audience on his side within seconds of starting.

At 6ft 4in, Dara Ó Briain is a massive bloke. With his bald, cannon-ball head and barrel-chested torso – togged out in a suit – he looks like a bulldog that's acquired a tailor. But it is not, of course, his physical build that has made this affable Irishman a huge name in the entertainment industry. What's key to his popular appeal is his "ordinary bloke" manner combined with his gift of the gab and his quick mind.

Bo Burnham says he doesn’t like the terms musical comic, internet sensation or teenage wonder. Well he’s all three, save the last now, as he turned 20 during this year’s Fringe - and anyway he prefers the term prodigy, he tells us in deadpan tones typical of the deeply ironic, faux offensive manner of his performance style. But sensationally talented he undoubtedly is, and this is an hour so stuffed with gags - verbal, visual and musical - that one almost doesn’t have enough time to savour each one before yet another rolls by.

With the charm-cum-cheek of a naughty schoolboy, Patrick Monahan is an instantly likeable presence whose latest show, I Walked, I Danced, Iran, is a lop-sided but very funny hour-and-a-bit of observational comedy. Monahan is a veteran of several Fringes and a regular on The Paul O’Grady Show on Channel 4.

When Sarah Millican won the If.comedy newcomer award two years ago, it was with one of the most accomplished shows I had ever seen at the Fringe - by newbie or veteran - and now the South Shields stand-up has made critics reach for the superlatives again with another hour of superbly crafted comedy.