Reason's Matt Welch says it well:
"Ever since election night of 2016, it has been clear that the Libertarian Party, through all its fits and starts over the decades, has managed to create a uniquely attractive prize: likely ballot access in all 50 states for a presidential candidate at a time of unusual major-party upheaval and discontent. All this for the low, low price of wooing fewer than 1,000 delegates at the 2020 national convention."
Here's a short list of 2020 possibilities:
Mitt Romney - We know he wants to be president. He's already ran, what twice now? Three times? He went as far as getting the Republican nomination for the U.S. presidency in 2012, after losing it to John McCain in 2008, but was defeated in a general election blowout by the sitting president, Barack Obama.
His quietly victorious 2018 campaign for U.S. Senate representing Utah puts Romney back on the national stage, leaving many to wonder whether his presidential aspirations may get the better of him again, but things are more interesting heading into 2020.
As The Atlantic notes:
"No other Republican of his stature denounced Trump in such raw language, with the goal of halting Trump’s march to the nomination."
Romney called Trump a "phony" and a "fraud."
So it's not difficult to imagine Mitt Romney attempting to lead one of those once-a-century epic U.S. political realignments, mounting a third party challenge as a Libertarian and pulling together a coalition of odd bed fellows to wreak some havoc on Trump's reelection bid, and maybe even forge the first viable path to the Oval Office for a third party candidate since Lincoln.
It's even less difficult to imagine when one remembers that Mitt Romney wanted the Libertarians to be on the debate stage in 2016, and nearly endorsed the Libertarian Party ticket of Gary Johnson and Bill Weld for president in 2016, and basically did endorse Bill Weld (who shares with Romney the distinction of being a fmr. Republican Governor of Massachusetts).
Now don't think he could seek the Libertarian Party's nomination without a forceful push back from many Libertarians, who would see it as a hostile takeover by a big government, tax-and-spend Republican, who would be using the Libertarian Party as a vehicle for his personal ambitions, not to advance libertarian principles. Gary Johnson and Bill Weld
Gary Johnson - Gary Johnson has ruled out running for president again in 2020, but he also ruled out running for Senate in 2018, until he was drafted to in the final stretch by the Libertarian Party of New Mexico. With two presidential bids at the top of the Libertarian Party ticket under his belt, for 2012 and 2016, fmr New Mexico Governor Gary Johnson is the most credible candidate the Libertarians have ever nominated to run for a public office.
Bill Weld - Bill Weld, the fmr. Massachusetts Governor and Vice Presidential candidate for the Libertarian Party in 2016, seems to have his eye on the top of the ticket for 2020, though he has not announced any plans yet. Weld has been traveling across the country on a tour of state LP conventions, telling Reason Magazine:
"I’m sincere when I say that I’m not talking about who is going to do the Libertarian race in 2020; I’m just here to say that I think that’s a race that has some real potential to go the distance, and the sooner we all wrap our minds around that, the better." bitcoinist
Patrick Byrne - The Founder and CEO of Overstock, a tireless critic of nefarious Wall Street practices (such as "naked" short selling) who has mounted more than one legal challenge to Wall Street firms, and a major advocate of private currencies, Patrick Byrne is also a libertarian who has given lectures at the libertarian Ludwig von Mises Institute in Alabama and the libertarian Cato Institute in Washington, DC, and was an enthusiastic supporter of Gary Johnson for President. Byrne has said he's not interested in running, but left open a "ten percent" chance that he might.
Larry Sharpe - Larry Sharpe– a business consultant, entrepreneur, and political activist– only narrowly missed being the vice presidential nominee of the Libertarian Party for 2016, and as its gubernatorial candidate in New York for 2018, secured ballot access for the Libertarian Party for state offices in New York for the next four years. He hasn't thrown his hat in the race yet, but Libertarians are expecting great things from him.