The Talmud and Jewish comedy are not often spoken about in the same breath. But for Alex Edelman, one of the hottest tickets at this year's Edinburgh Festival Fringe, it has been a key component in his comedic development. An Orthodox upbringing informs the work of the 26-year-old, Crouch End-based Bostonian, who won the Foster's Edinburgh comedy best new comer award last year for Millennial, his debut Edinburgh show.

Edelman's show at the Pleasance, Alex Edelman: Everything Handed to You, references his basic training as a teenager in the IDF while spending a year at a Jerusalem yeshivah. "The talmudic approach is a big part of how I approach things," he says. "I can't speak enough for how important it's been. It's a huge part of my life and my show. The talmudic approach is all about detail and the more detail you can access helps you comically.

"Jewish comedy is self-reflective. Simon Amstell does it very well. Woody Allen did it well. [Jerry] Seinfeld uses detail and is self-reflective." The Jewish experience is "a real blend of outsider and insider. You're part of a very close-knit group or community, with a strong cultural identity, but you're also an outsider wherever you are. It's a specific and sharp way of seeing the world.

Read: Jewish talent multi-tasks at this year's Edinburgh Fringe

"And being able to see the world from different angles, to see modern life from the point of view that it's not the most important thing, enables you to mock it a little more."

The Talmud also features in Ivor Dembina's comic awareness, though his concerns are more where Jewish comedy is at, and where it is headed, than where it has come from. The founder and host of the Hampstead Comedy Club - whose views on Israel and the Palestinians and support for a cultural boycott of Israel have placed him at loggerheads with the Jewish establishment - feels Jewish comedy is stuck in the past and needs to address "social, historical and political truths of the 21st century".

Dembina, 64, was in the second wave of the alternative comedy scene in the early 1980s.

In 1994, he was the first comedian to bring a solo Jewish show, Stand Up Jewish Comedy, to the Edinburgh Fringe. This year, his lunchtime show, Old Jewish Jokes ("Admission free... gentiles half-price" it says on the flyer) has been playing to packed audiences. He also has a New Jewish Jokes gig at teatime. He covers everything from domineering Jewish mothers ("How many Jewish mothers does it take to change a light bulb? None. You just sit there and suffer") to Israel ("Israel wants peace. A piece of Egypt, a piece of ...").

Its backdrop is a censorious rabbi wanting him to do a gig to raise money for a hole in the roof of his local synagogue, but cautioning him against bringing up a long list of sensitive subjects.

"The default position among diaspora Jews is conservatism, grounded in fear," he says. "Jews like to be modern or hip, but when it comes to hearing some challenging jokes about themselves they get nervous. Jewish humour is stuck in the past, which I regard as a pity. Modern Jewish comedians are too scared of offending their own community, but fear and true comedy can never coexist.

"If you want to push things a bit further and do jokes that challenge the boundaries of acceptable content, you expose yourself to condemnation from those who claim to know what's best for the Jewish community - our so-called leadership. Personally, I didn't come into comedy to become popular - I did it to tell the truth and make people laugh at the same time."

North Londoner Josh Rinkoff - a scion of the East End Rinkoff baking dynasty who performs as Harry Deansway - argues that making comedy out of hardship is a very Jewish trait. "Comedy for me is a way of processing difficult information," he says. In his show, he discusses being sued three times, having a "100 per cent sacking record" and at getting into £30,000 of debt running a comedy magazine. It is, he warns his audience, "a cautionary tale of how, if you fight the capitalist system, you'll end up, aged 35, living at home with your parents". He has literally just wrapped up a show by entangling his audience in a ball of red wool.

American-born Lynn Ruth Miller, 81, now lives in Brighton. She claims to be the oldest working stand-up either side of the Atlantic and believes Jewish and black comics have a similar way of looking at life, born of a shared history of prejudice and persecution.

"We do not internalise rejection - we make fun of it. Jews make fun of things others wouldn't. I make fun of my eating disorder. In one joke, my psychiatrist says to me: 'All you ever think of is food', and I say: 'Is there anything else to think of?'"

Miller was brought up by her immigrant parents in Toledo, Ohio, where she remembers an unsympathetic response to the suffering of the Jews in the Holocaust.

Her Edinburgh show is a bitter-sweet autobiographical cabaret in which she recalls two failed marriages, a constantly critical mother and a gentle but distant father.

They "aspired to status far more than they aspired to happiness", joining a Jewish country club "so they could feel upper class.

"I was a social failure and my mother told me that every day of her life. Now that I'm 81, I don't mind being a social failure: it makes me adorable," she told a preview audience of five.

Miller came into the comedy scene only a decade ago after working as a teacher, a professor of humanities, a "telephone madam" and a freelance writer.

"I'm a comedian because, if you listen to my life, I had two ways to go," she reflects. "I could have been a miserable, screaming bitch, or I could have made fun of it. I've always said: 'I laugh because otherwise I'd cry.' It comes out of the same source, which is pain."

For Brummie writer and performer Naomi Paul, Jewish comedy incorporates reflections on immigration and on identity. "I think all the stuff in the show about immigration, then and now - how you integrate and at what level - is relevant for everybody who comes here [to Britain]. The whole question of identity is part of that - who you think you are, where you are from.

"It surprises me that I have come out about being Jewish in performing. In the past, you might have not necessarily been so 'out' about it. Broadly speaking, Americans are much more out about it. Jewish humour is much more a part of American humour, here it is less so."

Alex Edelman: 'Everything Handed to You' is at Pleasance Courtyard until August 30

Ivor Dembina: 'Old Jewish Jokes, is at Laughing Horse@ Finnegan's Wake until August 29; 'New Jewish Jokes' is at the Stand Comedy Club 5&6 until August 30

Lynn Ruth Miller: 'Get a Grip' is at C Nova until August 31

'An Audience with Harry Deansway' is at Just the Tonic at The Tron until August 29

'Price Includes Biscuits' by Naomi Paul is at the Space@Surgeons' Hall until August 29