The US President went into the meeting with no set agenda that was made public, but it is reported he and Mr Putin spoke about a ceasefire in southwest Syria, Ukraine, the fight against terrorism, and cyber-security.
Ahead of meeting, Mr Trump said it was an “honour” to meet Mr Putin. The Russian leader, in turn, said that conversations over the phone were not enough to discuss all the matters at hand.
Tom Bernes, a Distinguished Fellow with the Centre for International Governance Innovation, told The Independent that the mood at the G20 was one of "curiosity" about what would be discussed in the meeting.
Mr Trump as the “Uncertainty Engine in the mix” is part of the issue in determining what will come out of the Trump-Putin meeting and the final document - the G20 Communique, Dr Stephen Saideman, an expert on the Western alliance at Canada’s Carleton University, told The Independent.
Given the personalities of the brash Mr Trump and the ex-spy Mr Putin, this is a matter of winning and losing in the one-on-one meeting.
Mr Putin “is likely to win” he said.
The US leader is facing pending FBI, House, Senate, and special prosecutor investigations into his campaign team’s alleged ties to Russian officials as well as obstruction of justice charges.
Mr Tillerson has said there was "positive chemistry" between the two leaders and that there was "not a lot of re-litigating of the past" between them. Much of the focus was how to "move the relationship forward".
Keir Giles, an Associate Fellow on Russian affairs at Chatham House, told The Independent that in not acknowledging past grievances - especially the topic of Russian interference in the 2016 US election - he is in a way "excus[ing] Russia [for] an absolutely inexcusable hostile action against the US".
Mr Tillerson noted Mr Trump opened the meeting with the issue, with Mr Putin denying Russia's role in it. According to Mr Lavrov, the US leader accepted the declaration, but that was not exactly the story on the US side.
"In the context of this meeting the US side has been unable, or quite possibly unwilling, to exercise deterrence in order to constrain Russia," Mr Giles said.
The Secretary of State, who spoke to reporters off-camera, said Mr Trump had repeatedly brought up the allegations.
He noted that the leaders discussed wanting a "framework" of some sort to "judge" cyber-security threats in light of the chaos caused by the hacking allegations and email leaks from the Democratic National Committee.
However, Mr Saideman commented that this idea may be a moot point if the Russians do not admit to the hacking activity.
Mr Trump and Mr Tillerson "want[s] to bury the hacking of the election for both domestic purposes and working with Russia. They see it as an obstacle, not as an attack that needs to be addressed," he explained.
Another point that is curious is that despite the lengthy meeting - which First Lady Melania Trump interrupted and tried to end after about an hour - the pressing threat of North Korea was not brought up, at least according to Mr Tillerson.
The President has repeatedly said North Korean leader Kim Jong-un and their ongoing tests of nuclear weapons was one of the most important issues for the security of the US. He has railed against the United Nations Security Council for its inaction and gone after China's President Xi Jinping on Twitter and in various speeches for continuing to trade with Pyongyang.
Mr Saideman said the President and Mr Tillerson's criticism of others is just "noise. ...[and] insincere. If it was important, it should have been discussed."
It seems though that both foreign ministers are calling the meeting as a success because of the Syrian ceasefire agreement. However, Mr Tillerson said "we'll see what happens in the ability to hold that ceasefire".
Russia has long-been one of Syrian President Bashar al-Assad's few allies and the Defence Ministry has noted that US warplanes will be treated as "targets" should they cross the Euphrates River.
According to Mr Giles, Moscow did indeed win "the manipulation game".
Mr Lavrov was quick to give his concise account to the Russian media, while Mr Tillerson was far more "reactive," Mr Giles said.
"In the absence of any credible US participant in the meeting, the Russian version is likely to stand."
Despite the US media's focus on the bilateral, it is not the biggest priority at the G20.
“In terms of substance, we’re not expecting much” to come out of the face-to-face, Mr Bernes noted.
Mr Bernes, who spent four decades as Canada’s representative to international financial institutions, said that Germany’s ambitions for the meeting were “modest” given their upcoming election, but Mr Trump’s election “threw a curveball”.
He explained that Germany wanted sustainability and a focus on Africa to be the main topics of the discussion, however “developments have forced protectionism and climate change to the forefront”.
What everyone is hoping is a “victory [in] not having a roll back from previous positions”. Nothing happening is almost a good thing at this point.
“It will be hard to gain consensus” given that the US president does not want more action on climate change besides a re-negotiation of the Paris Agreement that several countries have already said will never happen and his “America First” approach to US trade.
The document is expected to be issued after the end of the summit on 8 July.
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