The president and the comic's conversation touched on many topics, from the media's failure to adequately cover the Russian email hack of the DNC, to Republicans' plan to repeal Obamacare ("If you sign up now, you will have insurance for a year, which is better than not having insurance for a year"), to how Obama personally navigated issues of race during his presidency.
But the most striking part of the conversation came when Noah asked Obama if President-elect Donald Trump's stated plans to undo everything Obama worked for during his presidency have changed his plans for his post-presidential public life.
Obama answered that while he will give the Trump administration space to figure things out on their own, he will speak up if Trump's assaults on democracy and decency become too much to bear.
For example, if Trump moves to create a Muslim registry, which would be an unconstitutional act of discrimination that would additionally make it easier for ISIL and similar groups to recruit potential terrorists, or if Trump starts deporting American-born children of immigrants, Obama "may have something to say about that."
He didn't intentionally criticize President Bush, who has all but receded from the public eye since leaving office, but he did say "I don't anticipate that I suddenly just vanish" after his term ends. He will take a long vacation, and then get back to writing and speaking, and if he feels he needs to protect the country from Trump, he'll do what he can.
Watch the full interview here.
The Daily Show airs Mondays through Thursdays at 11/10c on Comedy Central.