At 7:04 a.m. ET, Putin's motorcade arrived at the summit site, Villa La Grange. While both leaders tend to run late, Putin was only four minutes behind his scheduled arrival, which came ahead of the American president.

Reporters shouted questions at Putin when he exited his car and was greeted by the Swiss president.

"Do you trust President Biden?" they asked. "How are you feeling sir?"

Putin did not engage.

-ABC News' Jordyn Phelps

Putin's plane landed in Geneva on Wednesday at around 12:30 p.m. local time (6:30 a.m. ET), as planned, ahead of his meeting with Biden.

The Russian president was seen descending a covered staircase from his jet to the tarmac, where several black cars comprising his motorcade awaited. He gave a small wave before getting in one of the cars. His motorcade departed the tarmac at 12:41 p.m. local time (6:41 a.m. ET).

Biden arrived in Geneva on Tuesday.

Swiss President Guy Parmelin is scheduled to greet Biden and Putin at Villa La Grange, where their much-awaited summit is taking place, at 1:10 p.m. local time (7:10 a.m. ET). Parmelin is then expected to deliver welcome remarks and pose for a photo with Biden and Putin before the two leaders begin their meeting.

-ABC News' Molly Nagle and Jordyn Phelps.

When Putin meets Biden on Wednesday in Switzerland, experts in Moscow say for all their differences, the two leaders want something similar from their first summit: to cool things down.

The U.S. and Russia's relations are the worst they have been since the Cold War and since 2016 in particular seem locked in almost permanent crises.

Biden has said he wants a more stable and predictable relationship with Russia, one that would allow it to focus on other foreign policy priorities that are more important to it, like taking a harder line with China. The Kremlin for its part has faced a continuous and intensifying barrage of sanctions-- the latest in April-- and with its crackdown on opposition at home and aggressive actions abroad is increasingly becoming a pariah with western countries.

Since coming to office, Russia has appeared to want to get Biden's attention. The president offered Putin the summit after Russia massed thousands of troops on Ukraine's border in April.

But now, having got Biden to the table, analysts said Putin has a clear proposal to deliver in Geneva: stay out of Russian domestic politics and Russia might act less troublesome abroad.

"The Kremlin wants to transition to a respectful adversarial relationship from a disrespectful one we have today," said Vladimir Frolov, a former diplomat at Russia's embassy in Washington and now a commentator on foreign affairs.

"That is, it wants to be treated the same way the Soviet Politburo was treated by the US in 1970-80s," Frolov told ABC News. "Meaning no name-calling" — such as Biden calling Putin a "killer" — "no personal sanctions on the leadership, no democracy lectures, regular personal summit meetings; respectful tone of discussions, no tangible support for Russian opposition."

It will not be an invitation for détente but instead to return to the later years of the Cold War when Putin was a KGB agent and the Soviet Union and the U.S. saw each other as enemies but tried to maintain a predictable relationship. And, crucially, where Russia was treated as an equal.

"For this, the Kremlin is prepared to promise to behave more responsibly," Frolov said.

"This seems to be in line with what the White House sees as a desirable deliverable," he continued. "So unless one of the leaders stormed out of the meeting shouting expletives, the summit would be a major success."

-ABC News' Patrick Reevell

Biden will go before the press corps alone following his summit with Putin in Geneva on Wednesday. He defended that choice by saying he doesn't want the attention to be on physical details, but rather the substance of their discussions from their own points of view.

"I don't want to get into being diverted by, did they shake hands? How far did they -- who talked the most and the rest," Biden said in England on Sunday. "He can say what he said the meeting was about and I will say what I think the meeting was about. That's how I'm going to handle it."

-ABC News' Justin Gomez

The summit between the two presidents ended earlier than expected. Biden was the first to leave -- giving a thumbs-up to reporters as he walked out.

He departed Villa La Grange for his hotel in the "Beast," the armored presidential limousine that had been idling outside.

The two men spent two hours and 38 minutes meeting together, according to the White House -- shorter than up five hours White House officials said their encounter might last.

Next, Putin is expected to hold a news conference. Biden will wait to begin his own press conference until his counterpart's concludes.