Former U.S. Secretary of State Henry Kissinger told CNN that Thatcher was a "tremendous prime minister. She was a great lady, she had very strong opinions. And to those of us who knew her over the decades, she was a very warm person, which is not the public image that is often given."
Thatcher's great achievement for Britain was its success in the Falklands crisis, he said, referring to the war over the disputed islands known to Argentina, which also claims them, as Las Malvinas.
"For the United States, it was her staunch loyalty and commitment to the Atlantic alliance -- she was a reliable and steady ally."
She was also one of the first leaders to see the way forward to ending the Cold War, he said, spotting the potential for a new kind of leader in Mikhail Gorbachev.
"I like Mr. Gorbachev. We can do business together," she said in December 1984, three months before he became Soviet leader.
Her dealings with former U.S. President Ronald Reagan, a fellow political conservative, were notably warm, Kissinger said.
"Margaret Thatcher, in her relationship with Ronald Reagan, gave it an additional personal dimension and it was unusually close, and they acted between themselves almost as if they were part of the same government."
Ending the Cold War
Gorbachev, too, paid tribute to a "great politician" with a strong voice, who helped shape 20th century history.
"Our first meeting, in 1984, marked the beginning of a relationship that was at times difficult, not always smooth, but on both sides serious and responsible," he said.
"Gradually, our relationship became more and more friendly. At the end, we were able to reach an understanding, and it was a contribution to the change in atmosphere between our country and the West and to the end of the Cold War."
Former U.S. President George H.W. Bush -- whose first years in the White House overlapped with the end of Thatcher's time as prime minister but who served as vice president at the height of her power and influence -- called her one of the "fiercest advocates of freedom and free markets."
He said in a statement that Thatcher was a leader of rare character who "carried high the banner of her convictions, and whose principles in the end helped shape a better, freer world."
Thatcher famously told Bush, "this is no time to go wobbly," as the first Gulf War loomed.
His son, former President George W. Bush, said that he and his wife, Laura, were grieving the loss of a "strong woman and friend" in Thatcher.
Reagan's widow, Nancy, said she was terribly saddened by the loss of a dear and trusted friend.
"Ronnie and Margaret were political soul mates, committed to freedom and resolved to end Communism.
"As prime minister, Margaret had the clear vision and strong determination to stand up for her beliefs at a time when so many were afraid to 'rock the boat.' As a result, she helped to bring about the collapse of the Soviet Union and the liberation of millions of people."
Former President Bill Clinton said Thatcher "understood that the special relationship which has long united our two nations is an indispensable foundation for peace and prosperity.
"Our strong partnership today is part of her legacy."
'Great hurt to Irish and British people'
But Northern Ireland politician and Sinn Fein leader Gerry Adams gave a very different view of Thatcher's legacy.
"Margaret Thatcher did great hurt to the Irish and British people during her time as British prime minister," he said in a statement.
"Working class communities were devastated in Britain because of her policies.
"Her role in international affairs was equally belligerent whether in support of the Chilean dictator (Agusto) Pinochet, her opposition to sanctions against apartheid South Africa; and her support for the Khmer Rouge.