Here's what they have in common, and what they don't:
Devoted online followings
Paul had a massive and loyal Internet following. His supporters voted for him early and often in online polls and liked him on social media at a rate that trumped most other candidates. Sanders showed signs of a similar online support Thursday when stories about him made up to 60 percent of Reddit's r/politics page, though he's clearly not yet on Paul's level here.
Both were opposed to the 2008 Troubled Asset Relief Program (TARP) bailout. In 2008, Paul said it would "only make the problem worse" and Sanders said if taxpayer money had to be used, it should be from "those people who have caused the problem, those people who have benefited from President George W. Bush's tax breaks for millionaires and billionaires."
Both have expressed views on foreign policy that involve less involvement rather than more. Sanders, for example, has said Middle Eastern countries should be involved in the majority of the fight against the Islamic State, and Paul has called the U.S. "an empire by any definition, and quite possibly the most aggressive, extended and expansionist in the history of the world." Both, accordingly, voted against the war in Iraq.
Despite being on different ends of the political spectrum, both men have been cautious of the country's surveillance apparatus. Paul has called for getting rid of the NSA, while Sanders said he was "deeply concerned" by some of the its actions.
Rand Paul ran for president in 1988 as a Libertarian before running for the Republican nomination in 2008 and 2012, and Sanders is an Independent (and self-described socialist) who is running for the Democratic nomination. Sanders does, however, currently caucus with Senate Democrats.
Both have made comments that police officers should scale back in some areas. Paul said "the Republic is no more" and we "now live a police state," and Sanders said during unrest in Ferguson, "it really does make it appear that the police department there is an occupying army in a hostile territory."
They're both okay with same-sex marriage for different reasons. Sanders is supportive of LGBT rights, and Paul doesn't think the government should even be involved in marriage, saying, "If two individuals want to call themselves married, fine and dandy, that's their business."
Basic beliefs about the role of government
Sanders doesn't necessarily have a problem with the government getting involved in things — hence "socialist" — and Paul generally does — hence "libertarian."
Paul is opposed to abortion rights; Sanders is not.
Paul had an "A+" rating with the NRA, and Sanders had an "F."
Paul is pretty much against higher taxes, while Sanders thinks the rich should pay more.