On 60 Minutes Sunday night, President Obama and outgoing Secretary of State Hillary Clinton "sat side by side, trading laughs and finishing each other's thoughts," a scenario both admit would have been "improbable" four years ago, says Peter Baker at The New York Times. (Watch the interview below.) 60 Minutes host Steve Kroft got the two onetime rivals to talk about current events, their complicated and enigmatic relationship, Clinton's health, and global affairs, but "the unusual joint interview... was noteworthy mainly because it happened." Here, five things to know about the high-profile, 30-minute sit-down:

1. Obama lauds her tenure at State — but is it an endorsement?
Obama's praise of Clinton was so effusive "it teetered on an endorsement of a 2016 presidential bid that is still an open question," says The Associated Press' Phillip Elliott. So Kroft went there, asking the "expiration date" on his endorsement. That was a roundabout way of delving into what we all want to know, says Joe Gandelman at The Moderate Voice: Was this Obama's "way of sending a signal that he may love Vice President Joe Biden and Biden may be his best political bud, but in 2016 he'd like to pass the Democratic Party torch to Clinton, if she decides to run"? Obama didn't take the bait: "You guys in the press are incorrigible — I was literally inaugurated four days ago, and you're talking about elections four years from now." But "intended or not, it was Obama laying hands on Clinton in every respect, simply because it was owed her," says Taylor Marsh at her blog. And Clinton didn't slam the door shut on the 2016 speculation, offering "no Shermanesque statement that she wasn't running. No 'no.'" So, we'll see.

2. Obama is trying to write the first draft of history on Clinton
Despite the insistence of the punditocracy, the Obama-Clinton sit-down "wasn't about the Democratic nomination in 2016," says David Zurawik in The Baltimore Sun. No, "it was President Obama using TV — and the folks at 60 Minutes happily allowing themselves to be used — to write the first draft of history on Clinton's performance as secretary of state." Specifically, in the "most immediate and partisan sense," Obama was slapping down the narrative Republican senators were trying to spin last week at the Benghazi hearings, in which a few said Clinton wasn't worthy of her office. And Kroft let him — at least it "sure didn't look like he was doing anything I would call journalism in his softball interview."

Obama explains why he wanted the interview in the first segment:

3. This was probably a win-win-win interview
The joint interview was Obama's idea, Kroft points out, and the press focused largely on its benefits for Clinton — "Big-shot departing White House aides usually get a small, private farewell from the boss," says James Warren at the New York Daily News, "but Hillary Clinton got a nationwide hug on 60 Minutes"; Mary Bruce and Dana Hughes at ABC News call it "something of a parting gift" from Obama to Clinton — but getting the two pillars of the Democratic Party to talk through their old, storied rivalry, even obliquely, was a big score for CBS, too. And it's hardly a bum deal for Obama, who got his fair share of laudatory comments from Clinton: The president is starting his second term with approval ratings in the low 50s, but Clinton is leaving the world stage with an enviable 69 percent approval rating (including 91 percent of Democrats and 37 percent of Republicans).

4. The Clinton-Obama feud is clearly over
Both politicians came across as serious policymakers, but the standout from the interview is that "there is clearly a chemistry between the two," says The Moderate Voice's Gandelman. Four years after a bitter primary nearly tore their party apart, this seems to signal "if not the 'marriage' of the Obama and Clinton wings of the Democrat party, at the very least a substantial and significant healing of the rift." The "flawlessly effortless" interaction between Clinton and Obama clearly demonstrated a "fierce bond" between the two that "cameras cannot lie about," says Taylor Marsh. The press, and even their aides and spouses, may have found this relationship "unimaginable" a few years ago, but at least between Obama and Clinton, 2008 is water long under the bridge.

5. Clinton's health is improving
Clinton is wearing glasses for the first time, instead of contact lenses, because of the "lingering effects from the concussion that are decreasing and will disappear," she told Kroft when he asked about her recent head injury and cranial blood clot. "But the doctors tell me that will all recede. And so, thankfully, I'm looking forward to being at full speed." There's no history of anything like this in her family, Clinton adds, so "I have a lot of sympathy now when I pick up the paper and read about an athlete or one of our soldiers whose had traumatic brain injury."

Clinton talks about her health, among other issues, in the second half of the interview: