Amy Schumer. Schumer is arguably the most natural fit to replace Stewart. She’s had a hugely successful show on Comedy Central (Inside Amy Schumer), her act revolves around playing with left-leaning topics (gender politics, discrimination and objectification) and she manages to pull in an almost equal amount of male and female viewers. She’s also in the new Judd Apatow film Trainwreck, which has a work-in-progress screening at SXSW, and that could push her brand into the US mainstream for good. Whether she really wants to commit to a four-day-a-week show that grinds up political news and repackages it satirically is another matter.

John Oliver.Probably the most successful Daily Show alum after Colbert, Oliver has taken his pithy, witty and incredulous British shtick over to HBO and managed to create what is effectively a weekly version of The Daily Show. He ably covered for Stewart on The Daily Show in 2014 and would be more than capable of picking up the mantle and continuing to riff on political idiocy four times a week. The big stumbling block for him coming back is HBO. The cable giant has made Oliver a staple of its political coverage, in which he serves as a more distinctly left-leaning and politically correct foil to the cranky and more volatile Bill Maher. He also may just prefer the weekly format: he turned down the chance to take over from Craig Ferguson on CBS’s 12.30am slot, instead opting for HBO. But the chance to take over the most anticipated satirical late-night spot (one where he has clear links and history) may prove too good an opportunity to turn down.

Ricky Gervais. Some early reports have mentioned the British comedian as a possible replacement for Stewart. A cursory look at his background may have had many scratching their heads as to why a comic who is known for pushing the boundaries of good taste and hasn’t done any form of political satire would be a good fit for the Comedy Central show. But what is often overlooked is that even Gervais’s controversial skits are performed in character, and like a less obvious Colbert, his target is almost always himself. But although Gervais has made an impact in the US mostly via his vitriolic, no-holds-barred Golden Globes-roasting hosting, he probably doesn’t fit as well as either Schumer or Oliver.

Amy Poehler. Poehler has connections to Comedy Central (she is an executive producer on Broad City), and she certainly fits the bill as a left-leaning comic who has the presenting chops and experience to host the show. Parks and Recreation is coming to an end on NBC, and a stint in the Comedy Central chair might suit her. She’s got a knack for developing talent (Broad City), and that’s something the Daily Show has made a name for itself by doing. The question is would being tied down to the daily news grind be something she’d want to do or be able to commit to?

Trevor Noah. The South African comedian is an outsider for the Comedy Central show. He only recently joined Stewart’s staff, on which he serves as one of the many contributors offering insightful, knowingly ham-fisted takes on the news. Stewart is known for his brazen desire to push diverse comics to the forefront of US television, but with Larry Wilmore in the slot after the Daily Show, and Noah a new recruit, it may be too early – just not the right time for him to step up. Having said that, there is a school of thought which predicts Comedy Central should and will go for a relative unknown.

Conan O’Brien. Conan is still wandering in the late-night wastelands at TBS. He may have garnered a committed and loyal bunch of followers online and IRL, but he never really became the new leading light of late night that he was predicted to be when he took over from Letterman on NBC. But as Letterman did when he moved from NBC to CBS, Conan would bring a ready-made audience to Comedy Central. The main stumbling block could be the fact Conan is well established. He’s been on late night for 20 years, in one capacity or another; he’s not the fresh, new talent Comedy Central will want to lead the show for the next decade and beyond. His appointment could feel like a stop-gap solution, and for Conan, who’s been burned by that kind of arrangement before, it may be one step too far.

Nobody. The Daily Show’s current roster boasts an array of diverse and able presenting talent. Aasif Mandvi, the aforementioned Trevor Noah, Samantha Bee, Jason Jones, Jordan Klepper and Jessica Williams all do a great job of complementing Stewart’s stewardship. Comedy Central may be tempted to try a rotating schedule that uses all of them to fill the void Stewart leaves behind. The problem with that is, at the moment, most people tune in to watch Jon Stewart, not the Daily Show itself, and late night is all about having an established and recognisable host. But so long as Jimmy Fallon continues to make a success of ripping up the late-night rulebook, it will remain an outside bet.