President Trump likes to improve the relationship of USA with Russia in order to reach his stratigic object, To Make America Great Again (MAGA). Just like what President Nixion did in 1970s to have China in the US side to oppose the former Soviet Union, President Trump is doing the opposit to unite Russia to be against China. However, today is different from the 1970s, a fast changing world - that people in the world prefer peace and economic growth than conflict and cold war. Such trend cannot be blocked regardless who are they, that has been determined.
No doubt both the presidents are smart men. President Putin was ~one hour late at the meeting, sending a clear message to the world that he was not care about this summit because he and his fellow Russians have been suffering for year due to the sanction imposed by the westerns including USA. However, President Trump was not unhappy with Putin's late showing up, albeit the fact his face expression was serious when he finally met Putin.
There are a lot of problems between the US and Russia, although President Trump likes to resolve them. President Putin seems to have some evidence unfavorbale for Mr Trump. Nobody can speculate what were talked about between them in the close door meeting. However, the joint press conference after the meeting are pretty successful, suggesting that some kind deal was made.