A career diplomat whose service in Washington began during the Cold War, Mr Kislyak is an established figure on the diplomatic circuit known for courteously but doggedly pushing Russia's position at lunches and policy forums.
The furore is more over what Mr Flynn and Mr Sessions have said - or not said - about their discussions with him, than the meetings and phone calls themselves.
Mr Sessions has removed himself from an FBI probe into alleged Russian meddling in the US election after failing to disclose two meetings with Mr Kislyak at his confirmation hearing. He rejects claims he was trying to mislead.
Michael Flynn was fired from the post of national security adviser after he misled the White House about his conversations with Mr Kislyak, allegedly regarding US sanctions.
'Obstreperous and inflexible'
Mr Kislyak is widely described as amiable but tough talking, and an effective networker at the fraught fault-line between the two powers.
"He likes to operate behind the scenes," John R Beyrle, US ambassador to Russia between 2008-12, told ABC news. "He's a professional diplomat, not a politician."
"He is very smart, very experienced, always well prepared," Nicholas Burns, a former under secretary of state who negotiated on Iran sanctions resolutions at the United Nations with Mr Kislyak, told the New York Times.
"But he could be cynical, obstreperous and inflexible, and had a Soviet mentality. He was very aggressive toward the United States."
Born in Moscow to Ukrainian parents, Mr Kislyak gained a degree in nuclear physics before moving into the foreign service.
He was first posted to the US in 1981, initially in the Soviet mission to the United Nations, and then in the embassy.
He returned to Moscow in 1989, holding various positions in the foreign ministry and focusing on arms control, before being posted to Brussels where he was ambassador to Belgium and representative to Nato at the same time.
After a five-year stint back in Moscow as deputy foreign minister, he began in his current posting in 2008, shortly before the election of Barack Obama.
Michael McFaul, who served in Washington in the Obama administration and then as US ambassador in Moscow from 2012-14, described him as one of the ambassadors that "does things" especially in regard to arms control, as well as hailing "fantastic lunches" at Mr Kislyak's residence.
"Some people complain about the ambassador - but his job is to represent his country and I think he does it fantastically well," he said, introducing him at an event at Stanford University in November.
When asked why the Russian media had covered the US presidential election in such detail, Mr Kislyak exclaimed "because it was fun! ...just kidding".
But at a dinner he hosted at his Washington residence in January he said his sense of humour had deserted him when he considered US-Russian relations, which he said were at their worst since the end of the Cold War.
Russia has vigorously denied suggestions by CNN, citing unnamed "current and former US intelligence officials", that Mr Kislyak is a "top spy and recruiter of spies".
A foreign ministry statement described the report as "an egregious media provocation and a stunning charge to level at a Russian diplomat".
Mr Sessions said Mr Kislyak seemed to him to be "pretty much of an old style, Soviet-type ambassador".
"We talked a little bit about terrorism as I recall. Somehow the subject of the Ukraine came up," he said.
"Russia had done nothing wrong in any area and everybody else was wrong with regard to the Ukraine. It got to be a little bit of a testy conversation at that point."
And Mr Kislyak himself? He has made clear that he sees conversations with Republicans and Democrats - whether or not they are working for presidential campaigns - as "normal diplomatic work".
"Our job is to understand and to know people," he told his Stanford audience.
"I personally have been working in the United Sates so long that I know almost everybody".