Elizabeth Warren had long been expected to announce a run for the Democratic nomination for president, from the progressive wing of the party. On Monday morning, the Massachusetts senator duly made it official.

The field of confirmed contenders is not yet crowded: the Maryland congressman John Delaney is the best known of those who have already formally pitched in, and he isn’t well known at all. But as the saying goes, no US senator ever looked in the mirror and did not see a president gazing back: a positively enormous group of politicians – senators, congressmen and women, governors, mayors – waits in the wings, seasoned with a few business billionaires, all seemingly fancying their chances of taking on Donald Trump and winning the White House back.

Here are 10 of the leading names in the spotlight … and some of those bubbling under.

Kamala Harris

The junior senator from California is building campaign machinery and has been visiting states that hold their nominating contests early. A former district attorney and state attorney general who has gained national attention for, among other things, her tough questioning of Trump supreme court pick Brett Kavanaugh, Harris is popular among young Democrats in Washington, internships in her office keenly sought and fought for. In a contest in which diversity is sure to play a key role – the party won sweeping House victories in the midterms by standing explicitly against Trumpism and attracting women and minorities – Harris’s African American and Indian ancestry could well be as much of a plus as her political fire and skill.

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Cory Booker

The first African American senator from New Jersey and a former mayor of the city of Newark has also been building campaign operations and speaking in early voting states. In Iowa in October, the Guardian listened as he warned against “sedentary agitation” and received rave reviews from his crowd. In New Hampshire in December, the Guardian watched as Booker tested out a “moral” message, avoiding a focus on Trump and telling his audience in Manchester: “This is not a time to meet hate with hate. It is not a time to meet darkness with darkness. The call of our country has always been love.” In a country bitterly divided by the indignities or otherwise of the Trump presidency, how effective such inspirational speechifying can be will be a fascinating thing to consider.

Kirsten Gillibrand

Facebook Twitter Pinterest Gillibrand: a strong voice in the Democrats’ center. Photograph: Aaron P. Bernstein/Reuters

The junior New York senator, a formidable fundraiser with a strong record on progressive priorities, is openly preparing a run. It has been reported that she is having surprising difficulty in attracting donations because of her role in the resignation of Al Franken, the popular Minnesota senator who faced allegations of sexual misconduct and resigned while heavyweight Republicans facing similar accusations, not least the president himself, stayed in their seats of power. Gillibrand, who arrived in the Senate when Hillary Clinton joined the Obama administration, remains a strong voice at the centre of the Democratic party.

Bernie Sanders

It pays to remember that Sanders isn’t actually a Democrat: an independent, self-proclaimed democratic socialist senator from Vermont, his run for the 2016 nomination against Clinton was a genuine surprise, an insurgency that gathered momentum, perhaps damaged the favourite and, at least in hindsight, seems to have offered clear signs of what the party was missing in the post-industrial states which flipped for Trump, handing him the presidency in the electoral college despite a beating in the popular vote. Sanders is now a progressive figurehead but also a Washington veteran used to how it all works. Some think that at 77, he’s too much a veteran. But Trump is 72, which suggests that these days, age is just a number.

Joe Biden

Facebook Twitter Pinterest Biden ran, unsuccessfully, in 1988 and 2008. Photograph: Rick Bowmer/AP

Barack Obama’s vice-president was a long-term Delaware senator before he went to the White House and is a Mount Rushmore-sized figure in the Democratic party. He has openly flirted with a run and gleefully engaged Trump in rather undignified arguments about who could beat up whom, perhaps showing in doing so the popular touch that has him leading early polls in important places like Iowa. On the downside, such leads may simply be down to name recognition, his status as the embodiment of the white, male party establishment may now not be the bonus of old, and by inauguration day in 2021, Biden will be 78. He has also run twice for president before, in 1988 and 2008. Neither ended well.

Sherrod Brown

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An intriguing Senate outsider, the Ohioan won re-election in November as Republicans dominated his Trump-voting state, partially as a result of openly proclaiming his “populist” bent. No president has won the White House without Ohio since Kennedy, a fact regularly trotted out in lists such as these, but Brown’s appeal to blue-collar voters should not be taken lightly and is part of regular talk-show discussions about whether or not he’ll run. He has some of the rumpled, outsiderish charm of Sanders, a factor which may or may not have informed Clinton’s consideration of him for her VP pick. He’s also not particularly well known nationally, which may have counted against him then and may do again this time. Similar things could be said, bar the bit about being rumpled, about the Minnesota senator Amy Klobuchar, another who shone in grilling Kavanaugh and who has admitted she’s thinking about a run.

Beto O’Rourke

Facebook Twitter Pinterest Beto O’Rourke narrowly lost to Ted Cruz in November. Photograph: Beto for Senate

The soon-to-be former congressman from El Paso is leaving Congress because he relinquished his House seat to challenge liberal bogeyman Ted Cruz for his seat in the Senate. O’Rourke lost, more narrowly than might be expected in such a deep-red state as Texas, yes, but all the same a defeat, something Trump has been quick to highlight as presidential talk swirls. A former punk rocker with a common touch and a half-Spanish, half-Irish name – which he has had to defend from allegations of seeking unearned authenticity – O’Rourke is also, by current Democratic standards and not surprisingly given his coming from Texas, something of a centrist prone to voting with Republicans. On the left of the party, that is attracting rising disapprobation.

Julian Castro

A former mayor of San Antonio and a Housing and Urban Development secretary under Obama, the Texan twin of congressman Joaquin Castro was another touted as a possible running mate for Clinton. Like O’Rourke, he is relatively young and could conceivably enter VP territory this time around. He has said he is exploring a run and will announce either way in January. If successful, he would be the first Hispanic nominee for president. A charismatic speaker, his moves will be worth watching, though he remains an outsider for now.

Michael Bloomberg

Facebook Twitter Pinterest For the billionaire Bloomberg, funding would not be a problem. Photograph: Christophe Ena/AP

The billionaire former New York mayor is openly considering a run, which he could obviously fund formidably, has registered as a Democrat and has been visiting early voting states. Driven by the need for the US to assemble a coherent plan to tackle climate change, he has had little difficulty ranging himself against the coal-friendly, regulation-ripping president. On Sunday, Bloomberg told NBC he will make climate change a leading issue in the 2020 race, whether or not he runs. He might not be the only billionaire to do so: Tom Steyer is funding ads demanding Trump’s impeachment while he decides whether to pitch in, while even the Dallas Mavericks-owning, rugby-loving Mark Cuban has said he’s considering a go. The former Starbucks chief Howard Schultz also seems to fancy his chances. Oprah Winfrey, alas, has said she is out.

Eric Garcetti

Garcetti, son of Gil, the harassed district attorney in The People v OJ Simpson, is the man in charge of Los Angeles, the biggest city in the most populous state that is now almost all-blue, a bastion of progressive policies – not least in the face of the frightening effects of climate change – and fierce opposition to Trump. A run from such a platform could be interesting. There are other mayors and ex-mayors out there: from New York could come Bill de Blasio, a Clinton ally whose view of himself as a national figure angers some in his city, while from New Orleans may come Mitch Landrieu, his centrist reputation burnished by his sure handling of controversy over the city’s Confederate past and statues. From South Bend, Indiana, meanwhile, there is Pete Buttigieg: young, gay, progressive, determined, from the Rust Belt and quite likely not a strong candidate this time around at least.

And the rest …

As mentioned, the Maryland congressman John Delaney has declared his bid for the Democratic nomination. So, as it happens, has Andrew Yang, an entrepreneur from New York state, and Richard Ojeda, a military veteran who lost a bid for Congress in West Virginia.

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Everyone else is either discussing the issue with their wife/family/loved ones/pets, exploring it actively or not, considering it or archly refusing to comment. Among senators there is also Jeff Merkley of Oregon, a progressive stalwart. Eric Holder, Obama’s attorney general, hasn’t ruled it out; nor has John Kerry, a former Massachusetts senator, the 2004 Democratic nominee against George W Bush and Obama’s second secretary of state.

The Ohio congressman Tim Ryan has said he is interested, as has the Hawaii representative Tulsi Gabbard. The media has enjoyed talking up Stacey Abrams, beaten narrowly in a controversial Georgia gubernatorial election this year, and Andrew Gillum, narrow loser in a similarly nasty fight for the governorship in Florida. Among governors and former governors, Steve Bullock, of the otherwise resolutely red state of Montana, seems to be very interested; so does John Hickenlooper of Colorado, a cross-party pal of John Kasich, the Ohio Republican who looks set to primary Trump. Former Maryland governor and 2016 candidate Martin O’Malley told the Guardian he was thinking about another run; former Virginia governor Terry McAuliffe, a pillar of the party and former Clinton fundraiser, all but told CNN he was in on Sunday.

That, believe it or not, is not everyone. But one more name seems worth a mention. Some allies and aides have said Hillary Clinton might consider a third run for the White House. No, really.

• This article was amended on 31 December 2018. An earlier version referred to O’Rourke’s voting record attracting “rising approbation” on the left of the party. That should have said “rising disapprobation”.