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They’re friends. They’re strangers. They talk. They don't talk.

It's not entirely clear.

The on-again, off-again relationship between Donald Trump and Russian President Vladimir Putin is either a figment of the Republican presidential nominee’s imagination or a bad bromance between two alpha males.

But even if it’s true they’re not locking lips like they are in a mural painted on the side of a Lithuanian barbecue joint, public utterances suggest Trump and Putin are in a mutual admiration society of sorts — and have been on each other's radars for years.

People walk past a mural on a restaurant wall depicting Republican presidential hopeful Donald Trump and Russian President Vladimir Putin greeting each other with an passionate kiss in the Lithuanian capital Vilnius. PETRAS MALUKAS / AFP - Getty Images

In response to an inquiry from NBC News, a Kremlin spokesman insisted Putin and Trump haven't spoken.

"We've said it many times before, President Putin has never had any contacts with Trump, never spoken to him, including by telephone," Dmitry Peskov said. "The same goes for all of his staff."

Here’s a timeline of the relationship — whatever it may really be:

June 18, 2013: Trump muses about becoming bosom buddies with Putin.

"Will he become my new best friend?" Trump asked of Putin in a tweet wondering whether the Russian leader would attend the 2013 Miss Universe pageant Trump brought to Moscow.

Do you think Putin will be going to The Miss Universe Pageant in November in Moscow - if so, will he become my new best friend? — Donald J. Trump (@realDonaldTrump) June 19, 2013

October 3, 2013: Trump says Putin is "outsmarting" the U.S.

"I think he's done really a great job of outsmarting our country," Trump told Larry King after Putin dissuaded the U.S. from attacking Syria by arranging for the removal of President Bashar Assad's chemical weapons.

March 21, 2104: Trump says Putin will restore the Russian empire.

I believe Putin will continue to re-build the Russian Empire. He has zero respect for Obama or the U.S.! — Donald J. Trump (@realDonaldTrump) March 22, 2014

April 17, 2014: Trump praises Putin and trashes President Obama.

America is at a great disadvantage. Putin is ex-KGB, Obama is a community organizer. Unfair. — Donald J. Trump (@realDonaldTrump) April 17, 2014

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July 31, 2015: Trump says he'd "get along very well with Vladimir Putin."

"I just think so," Trump told reporters in Scotland. "People say, 'What do you mean?' I think I would get along well with him,"

"He hates Obama, Obama hates him. We have unbelievably bad relationships. Hillary Clinton was secretary of state. She was the worst secretary of state in the history of our country. The world blew apart during her reign. Now she wants to be president," Trump added.

Oct. 11, 2015: Trump says he and Putin bonded on same episode of "60 Minutes."

"I think the biggest thing we have is that we were on '60 Minutes' together and we had fantastic ratings. One of your best-rated shows in a long time," Trump said. "So that was good, right? So we were stablemates."

Trump says he and Putin "are very different," but that they would "get along very well."

"I think that I would probably get along with him very well. And I don't think you'd be having the kind of problems that you're having right now," Trump says.

Nov. 10, 2015: Trump insists again he and Putin became "stablemates" on "60 Minutes."

"I got to know him very well because we were both on '60 Minutes,' we were stablemates, and we did very well that night," Trump said.

(Never mind that Trump and Putin were in different countries — and interviewed at different times — for the same show. Trump stuck to the story during a GOP debate.)

Dec. 17, 2015: Putin and Trump heap praise on each other.

“He’s a very lively man, talented without doubt,” Putin told reporters in Moscow, referring to Trump as the “absolute leader in the presidential race.”

"It is always a great honor to be so nicely complimented by a man so highly respected within his own country and beyond," Trump said a few hours later. "I have always felt that Russia and the United States should be able to work well with each other towards defeating terrorism and restoring world peace, not to mention trade and all of the other benefits derived from mutual respect."

Dec. 18, 2015: Trump defends Putin against allegations the Russian leader has ordered the killings of journalists.

"He's running his country and at least he's a leader, unlike what we have in this country," Trump said on MSNBC's "Morning Joe." "I think our country does plenty of killing also."

Feb. 17, 2016: Trump says he'd be "crazy" to disavow Putin's praise.

"I have no relationship with him other than he called me a genius. He said Donald Trump is a genius and he is going to be the leader of the party and he's going to be the leader of the world or something," Trump said, embellishing Putin's praise.

"These characters that I'm running against said, 'We want you to disavow that statement.' I said, 'What, he called me a genius, I'm going to disavow it? Are you crazy?' Can you believe it? How stupid are they?"

"And besides that, wouldn't it be good if we actually got along with countries? Wouldn't it actually be a positive thing? I think I'd have a good relationship with Putin. I mean, who knows," he continued.

April 28: Trump says maybe they'll get along.

"Maybe we will, maybe we won't," Trump says when asked by Bill O'Reilly about whether he and Putin would have a nice relationship.

"I'm saying that I'd possibly have a good relationship. He's been very nice to me," Trump said. "If we can make a great deal for our country and get along with Russia that would be a tremendous thing. I would love to try it."

June 17: Putin calls Trump “bright” at the Russian Economic Forum in St. Petersburg.

July 25: Trump suggests the Russians are behind the WikiLeaks publication of 20,000 internal Democratic National Committee emails. The reason, according to Trump? Putin "likes" him.

The new joke in town is that Russia leaked the disastrous DNC e-mails, which should never have been written (stupid), because Putin likes me — Donald J. Trump (@realDonaldTrump) July 25, 2016

July 27: Trump suddenly insists he and Putin have never met.

“I never met Putin, I don’t know who Putin is,” he said at a Florida news conference. “He said one nice thing about me. He said I’m a genius. I said ‘Thank you very much’ to the newspaper, and that was the end of it. I never met Putin.”

July 28: Trump says he wouldn’t be Putin’s patsy.

"I would treat Vladimir Putin firmly, but there's nothing I can think of that I'd rather do than have Russia friendly, as opposed to the way they are right now, so that we can go and knock out ISIS with other people," Trump said at a news conference.

Trump, who was catching heat after urging Russia to “find” the missing emails from Hillary Clinton’s private server, also refused to call on Putin to steer clear of the U.S. presidential election.

"I'm not going to tell Putin what to do,” he said. “Why would I tell him what to do? Why do I have to get tough on Putin? I don't know anything other than that he doesn't respect our country.”

Trump also said Putin would respect him more than Clinton.

"I don't think he has any respect for Clinton,” he said. “I think he respects me. I think it would be great to get along with him.”