They are of a similar age, and both consider themselves modernisers.
The British Prime Minister, Tony Blair, who arrives in Moscow on Monday on a two-day official visit, is assured of a warm welcome.
This is both because of his good personal relations with President Vladimir Putin and because of Mr Blair's approach to the Chechnya conflict.
But Mr Blair will also be stepping into a controversy over US missile defence plans which have deeply angered Russia.
It will require a difficult balancing act.
Personal chemistry
Tony Blair was the first European leader to develop a close working relationship with Vladimir Putin, even before he was elected president.
The two men now have a good personal chemistry.
They are of a similar age, and both consider themselves modernisers.
More importantly, they have both presented ambitious agendas and raised expectations.
Some Western countries put their contacts with Moscow on hold as a result of Moscow's policies towards separatist Chechnya, where a bloody war has raged for more than a year.
But Mr Blair decided to maintain contacts with Moscow, even when domestic critics said he was making a mistake.
That decision seems to have been appreciated by President Putin.
The Russian President has used his visits abroad to lobby hard for investment in Russia.
Mr Putin likes to tell Western audiences that he is committed to economic reform, and that there will be no turning back to the past under his leadership.
Defusing a row
But during this visit, the UK prime minister will be focusing on another subject - Russia's relationship with the United States.
Russia is annoyed at US plans to develop new space-based anti-missile defence systems.
The plan looks like a revival of the 1980s 'Star Wars' idea.
That was promoted hard by then-President Ronald Reagan, but technology meant it could not become a reality.
But technology has advanced and the scheme may now be feasible.
But Moscow insists that such a system would be a violation of the 1972 Anti-Ballistic Missile treaty, which was signed by the US and the Soviet Union.
Washington off-guard
And Moscow has used the current uncertainty over the final outcome of the US election to propose drastic new cuts in missile numbers.
It has caught the US establishment off-guard.
New weapons cuts would make the scheme proposed by the US unnecessary.
But behind the public anger, Moscow also realises that it just would not be able to match US technology.
Tony Blair has offered to moderate between the US and Russia over the missile-defence plans.
He says he understands both sides' concerns.
But the US radar installations in the UK would form part of the defence shield, and London still likes to say it has a 'special relationship' with Washington.
Britain is not likely to do anything to undermine its strategic relationship with the US.
But Moscow also has real demands, and it wants to make them heard through whatever means it can.
That includes the British prime minister, who is a valued partner in Russia's foreign policy strategy.