Who will replace Jon Stewart on the Daily Show?

"This show doesn't deserve an even slightly restless host, and neither do you," said Jon Stewart, announcing his decision to step down from The Daily Show.

He joined the nightly news satire in 1999 as a stand-up, but leaves as one of America's most listened-to political commentators, and a bete-noire of the conservative establishment.

His departure leaves a big hole in the show, and Comedy Central will be relieved that Stewart has yet to set an end date.

Speaking on the show last night, Stewart said his contract runs out in September, but his final show "might be in December, might be July. We're still working out details".

But who will fill his seat? The most likely candidates - Steven Colbert and Larry Wilmore - have recently taken new jobs, effectively ruling them out of the running.

Here are some of the other possible runners.

Jessica Williams

The Daily Show's youngest reporter, Williams is a graduate of the Upright Citizens Brigade Theatre, the comedy "improv" troupe set up by Amy Poehler.

Variously labelled the show's "senior youth correspondent" and "senior Beyonce correspondent", she has already displayed the combination of razor sharp wit and humanity that the host requires.

Her expose of the abuse women suffer on the streets of New York was powerful; while her response to the shooting of unarmed teenager Jordan Davis was elegantly concise.

Writing in Wired Magazine last year, she outlined her desire to create a new celebrity gossip site that, coincidentally, sounded like a manifesto for the future of the Daily Show.

"There's something missing in all this new media craziness, and that is something that uses celebrity news as a way to get into a really serious analysis of our culture," Williams said.

"The Kardashians are walking clickbait - but let's look closer. Do Kim and Kanye affect how society feels about interracial relationships and blended families? What does our obsession with Jennifer Lawrence say about third-wave feminism?

"Start with a headline that's superjuicy; a flashy, sexy picture. And then, after the first couple of lines, hit them with some really severe analysis."

A petition to have Williams installed in the hot seat is already up and running.

John Oliver

A successful run as The Daily Show's "senior British correspondent" landed Oliver an eight-week stint as host in 2013, when Stewart took a hiatus to direct his first movie, Rosewater.

Many had doubts about his ability to sustain the show but, in fact, he succeeded in pulling off the tricky mix of insight, humour and pathos the show requires.

He was particularly lucky to be hosting during a royal birth, providing plenty of opportunities to skewer the breathless 24-hour news coverage while playing up his British roots.

Oliver also extended a personal "thank you" to New York Mayoral candidate Anthony Weiner (aka Carlos Danger), whose sexting scandal provided days of juicy material.

The comedian's tenure was so successful that Stewart phoned the show to say watching him was "like watching someone have sex with your wife's desk".

It also earned him his own weekly satirical programme on HBO - making a return unlikely for now.

Jason Jones

Canadian comedian Jason Jones is one of The Daily Show's most astute correspondents, something he's proved with assignments in Russia, Iran and India over the past four years.

The Iran trip, which took place a week before the disputed 2009 elections and subsequent Green Revolution, was both satirical and poignant, with many of his interviewees later arrested and questioned by police.

In Moscow, he asked Vladimir Putin's spokesperson Sergey Markov about gay rights, eliciting the response: "I'm tired from (sic) this issue! You are absolutely free to make sex with this table!"

Jones then bagged an interview with Mikhail Gorbachev and suggested that, in an era of terrorism, he longed for the stability of the Cold War's "them and us" dynamic.

After he implored Gorbachev to "put back that wall", the former Soviet leader demanded: "Who asked for this meeting? If you bring cameras in here again, I will put you against the wall."

One of The Daily Show's most reliable contributors, Jones has hosted the programme once, when Stewart was ill - although it did not go down well.

With more grooming and better preparation, however, he could be a candidate for the hot seat.

Amy Schumer

Schumer is one of US comedy's hottest young talents. She's already got her own show on Comedy Central and will be hosting the MTV Awards later this year.

Her humour tends to skew towards the personal - one sketch on her TV show finds her praying to God that she doesn't have herpes. God, aka Paul Giamatti, appears and says: "70 percent who reach out to me are having a herpes scare."

But she also tackles bigger, thornier issues. In one segment, she decided to play a Call of Duty-style "realistic military game".

But when she chose a female character, she didn't get to run around blowing things up. Instead, her character was raped - and when she tried to get her assailant convicted, she was faced with form-filling bureaucracy and a concerted campaign of character assassination.

Inside Amy Schumer was the most watched series premiere for Comedy Central in 2013, and her name was bandied around when Stephen Colbert deserted his show last year.

Chris Rock

An unlikely choice, perhaps, but Chris Rock has a passion for politics and pop culture combined with a fierce sense of humour.

Speaking to Vulture last year, he delivered this assessment of Barack Obama's presidency: "There's an advantage that Bush had that Obama doesn't have. People thinking you're dumb is an advantage.

"Obama started as a genius. It's like, 'What? I've got to keep doing that? That's hard to do!' So it's not that Obama's disappointing. It's just his best album might have been his first album."

But - apart from the fact that Comedy Central probably couldn't afford him - Rock has effectively ruled himself out of the race.

"I always had, like, a dumb-guy's view of current events," he told Rolling Stone last year. "Always kind of know a little bit of what's going on. If I knew any more about current events, I probably wouldn't talk about it.

"I had to stop going on the Bill Maher [talk] show. Too smart. I'm on, like, the barbershop level."

Other potential candidates

Many of The Daily Show staff will be buffing up their showreels as Stewart takes his long, slow walk to the exit door.

Aasif Mandvi has been a regular on the show since 2006, and would be in a strong position; while John Hodgman makes an impact every time he appears - although he may prove a little too arch for the main job.

Comedy Central could try to tempt back former alumni such as Rob Riggle, Rob Cordry or Olivia Munn; while US media have been positing more established names like Sarah Silverman, Amy Poehler and Aziz Ansari in connection with the role.

Michael Che, who presents the topical "weekend update" segment on Saturday Night Live has the requisite overview of current affairs, while NBC anchor Brian Williams might be looking for work in the coming months.

Variety Magazine suggests British comedian Ricky Gervais could be in with a shot; and it's not outside the realms of possibility that Armando Iannucci and Chris Addison could be considered, following their work on US presidential satire Veep.